<div class="question xl:text-lg px-4 py-2.5">P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.4%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mi>d</mi><mi>r</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>. The quantitative ketch of the dependence of P on r is</div><div class="question xl:text-lg px-4 py-2.5">P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.4%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D70B TEX-I"></mjx-c></mjx-mi><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D451 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D45F TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mi>d</mi><mi>r</mi></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>. The quantitative ketch of the dependence of P on r is</div>