omron-sinicx/MaterialBENCH huggingface dataset:
Problem: The electrical conductivity and electron mobility for aluminum are 3.8 x 10^7 (Ω∙m)^-1 and 0.0012 m^2/V∙s, respectively. Calculate the Hall voltage (V) for an aluminum specimen that is 15 mm thick for a current of 25 A and a magnetic field of 0.6 tesla (imposed in a direction perpendicular to the current).
Answer: -3.16 x 10^-8
Problem: Consider a parallel-plate capacitor having an area of 6.45 x 10^-4 m2 and a plate separation of 2 x 10^-3 m across which a potential of 10 V is applied. If a material having a dielectric constant of 6.0 is positioned within the region between the plates, calculate the capacitance (F) and the magnitude of the charge (C) stored on each plate.
Answer: 1.71 x 10^-11, 1.71 x 10^-10
Problem: A copper wire 100 m long must experience a voltage drop of less than 1.5 V when a current of 2.5 A passes through it. Electrical conductivity of copper is 6.0 x 10^7 [(Ω∙m)^-1].  calculate the minimum diameter (mm) of the wire.
Answer: 1.88
Problem: electrical conductivity of copper is 6.0 x 10^7 [(Ω∙m)^-1]. What would be the current flow (A) of a copper wire 3 mm in diameter and 2 m long if the potential drop across the ends of the wire is 0.05 V?
Answer: 10.6
Problem: At room temperature the electrical conductivity and the electron mobility for copper are 6.0 x 10^7 (Ω∙m)^-1 and 0.0030 m^2/V∙s, respectively.
Calculate the number of free electrons per cubic meter for copper at room temperature. Assume a density of 8.9 g/cm3.
Answer: 1.25 x 10^29
Problem: An n-type semiconductor is known to have an electron concentration of 3 x 10^18 m^-3. If the electron drift velocity is 100 m/s in an electric field of 500 V/m, calculate the conductivity ([Ω∙m]^-1) of this material.
Answer: 0.096
Problem: The following electrical characteristics have been determined for both intrinsic and p-type extrinsic indium phosphide (InP) at room temperature:
               σ  (Ω∙m)^-1   n (m^-3)   p (m^-3)
Intrinsic 2.5x10^-6    3.0x10^13    3.0x10^13
Extrinsic(n-type) 3.6x10^-5    4.5x10^14    2.0x10^12
Calculate electron and hole mobilities (m2/V∙s).
Answer: 0.50, 0.02
Problem: How the conductivity changes when temperature increase, for metals and intrinsic semiconductors, respectively?
Answer: metals: decrease; semiconductors: increase
Problem: A metal alloy is known to have electrical conductivity and electron mobility values of 1.5 x 10^7 (Ω∙m)^-1 and 0.0020 m2/V s, respectively. Through a specimen of this alloy that is 35 mm thick is passed a current of 45 A. What magnetic field (T) would need to be imposed to yield a Hall voltage of -1.0 x 10^-7 V?
Answer: 0.58
Problem: A parallel-plate capacitor using a dielectric material having a dielectric constant of 2.5 has a plate spacing of 1 mm. If another material having a dielectric constant of 4.0 is used and the capacitance is to be unchanged, what must be the new spacing (mm) between the plates?
Answer: 1.6
Problem: For NaCl, the ionic radii for Na  and Cl ions are 0.102 and 0.181 nm, respectively. If an externally applied electric field produces a 5% expansion of the lattice, calculate the dipole moment (C∙m) for each Na –Cl  pair. Assume that this material is completely unpolarized in the absence of an electric field.
Answer: 2.26 x 10^-30
Problem: A charge of 3.5 x 10^-11 C is to be stored on each plate of a parallel-plate capacitor having an area of 160 mm2 and a plate separation of 3.5 mm.
What voltage (V) is required if a material having a dielectric constant of 5.0 is positioned within the plates?
Answer: (a) V   17.3
Problem: A brass rod is to be used in an application requiring its ends to be held rigid. If the rod is stress free at room temperature (20 ℃), what is the maximum temperature (℃) to which the rod may be heated without exceeding a compressive stress of 172 MPa? Assume a modulus of elasticity of 100 GPa for brass.
Answer: 106
Problem: For aluminum, the heat capacity at constant volume at 30 K is 0.81 J/mol∙K, and the Debye temperature is 375 K. Estimate the specific heat (J/kg∙K) at 50 K and at 425 K.
Answer: 139, 923
Problem: For each of the following pairs of materials, decide which has the larger thermal conductivity by inequality sign.
(1) Pure copper; aluminum bronze (95 wt% Cu–5 wt% Al)
(2) Fused silica; quartz
(3) Linear polyethylene; branched polyethylene
Answer: (1)>, (2)<, (3)>
Problem: If a rod of 1025 steel 0.5 m long is heated from 20 to 80 ℃ while its ends are maintained rigid, determine the magnitude (MPa) and the type of stress that develops. Assume that at 20 ℃ the rod is stress free.
Answer: 150, compression
Problem: Railroad tracks made of 1025 steel are to be laid during the time of year when the temperature averages 10 ℃. If a joint space of 4.6 mm is allowed between the standard 11.9-m-long rails, what is the hottest possible temperature (℃) that can be tolerated without the introduction of thermal stresses?
Answer: 42.2
Problem: Calculate the saturation magnetization (A/m) for nickel, which has a density of 8.90 g/cm3.
Answer: 5.1 x 10^5
Problem: Calculate the saturation magnetization (A/m) for Fe3O4 given that each cubic unit cell contains 8 Fe2+ and 16 Fe3+ ions, and that the unit cell edge length is 0.839 nm.
Answer: 5.0 x 10^5
Problem: Design a cubic mixed-ferrite magnetic material that has a saturation magnetization of 5.25 x 10^5 A/m. Which ion should be used for replacing Fe 2+ and what content?
Answer: Mn2+, replace 18.1 at% of the Fe2 in Fe3O4
Problem: A coil of wire 0.20 m long and having 200 turns carries a current of 10 A.
What is the magnitude of the magnetic field strength H (A turns/m) ?
Answer: 10000
Problem: The magnetic flux density within a bar of some material is 0.435 tesla at an H field of 3.44 x 10^5 A/m. Calculate the magnetic susceptibility for this material.
Answer: 6.0 x 10^-3
Problem: Calculate the saturation magnetization (A/m) for cobalt, which has a net magnetic moment per atom of 1.72 Bohr magnetons and a density of 8.90 g/cm3.
Answer: 1.45 x 10^6
Problem: The chemical formula for manganese ferrite may be written as (MnFe2O4)8 because there are eight formula units per unit cell. If this material has a saturation magnetization of 5.6 x 10^5 A/m and a density of 5.00 g/cm3, estimate the number of Bohr magnetons associated with each Mn2+ ion.
Answer: 4.6
Problem: The following data are for a transformer steel:
H (A/m)   B (teslas)
0    0 
10    0.03 
20    0.07
50    0.23 
100    0.70 
150    0.92
200    1.04
400    1.28
 600    1.36
800    1.39
1000    1.41
What are the values of the initial permeability (H/m) and initial relative permeability? Answer in the style [initial permeability, initial relative permeability].
Answer: 3 x 10^-3 , 2388
Problem: The fraction of nonreflected light that is transmitted through a 200-mm thickness of glass is 0.98. Calculate the absorption coefficient (mm^-1) of this material.
Answer: 1.01 x 10^-4
Problem: Calculate the velocity of light (m/s) in calcium fluoride (CaF2), which has a dielectric constant of 2.056 (at frequencies within the visible range), and a magnetic susceptibility of  -1.43 x 10^-5. 
Answer: 2.09 x 10^8
Problem: The indice of refraction of a soda–lime glass within the visible spectrum is 1.51. determine the fraction of the relative dielectric constant at 60 Hz that is due to electronic polarization, using the data of the table below. Neglect any orientation polarization effects.
----------------------------------
Materials   Dielectric constant at 60 Hz   at 1MHz
soda-lime glass   6.9   6.9
fused silica   4.0   3.8
------------------------------------
Answer: 0.33
Problem: Using the data in the table below, estimate the dielectric constant for polypropylene,
Material   Index of reflaction
borosillicate glass   1.47
polypropylene   1.49
polyethylene   1.51
Answer: 2.22
Problem: The fraction of nonreflected radiation that is transmitted through a 10-mm thickness of a transparent material is 0.90. If the thickness is increased to 20 mm, what fraction of light will be transmitted?
Answer: 0.81
Problem: The transmissivity T of a transparent material 20 mm thick to normally incident light is 0.85. If the index of refraction of this material is 1.6, calculate the thickness of material (mm) that will yield a transmissivity of 0.75. All reflection losses should be considered.
Answer: 67.2
Problem: Calculate the difference in energy (eV) between metastable and ground electron states for the ruby laser.
Answer: 1.78
Problem: What was the original length (m) of a wire that has been strained by 30% and whose final length is 1 m?
Answer: 0.77
Problem: The initial diameter of a wire is 2 cm and needs to be reduced to 1 cm. Calculate the amount of cold work (reduction in area in percent) which is necessary.
Answer: 75
Problem: Calculate the initial diameter of a wire (cm) that has been longitudinally strained by 30% and whose final diameter is 0.1 cm. Assume no volume change.
Answer: 0.114
Problem: What force (N) is needed to plastically deform a wire of 2 cm diameter whose yield strength is 40 MPa?
Answer: 1.26*10^4
Problem: Calculate the Poisson ratio for the case where no volume change takes place.
Answer: 0.5
Problem: Calculate the number of atoms for an HCP unit cell.
Answer: 2
Problem: State the slip plane (in form of { }) and the slip direction (in form of < >) in a hypothetical simple cubic lattice.
Answer: {100}<100>
Problem: Determine the coordination number for the CsCl crystal structure.
Answer: 8
Problem: Calculate the packing factor for diamond cubic silicon.
Answer: 0.34
Problem: Calculate the planar packing fraction in the (111) plane in the FCC structure.
Answer: 0.907
Problem: Derive an expression for the distance between two nearest face atoms of the conventional FCC unit cell in terms of the lattice constant a.
Answer: √2/2a
Problem: Calculate the ratio between the diffusion rates of grain boundary diffusion and volume diffusion assuming an activation energy for grain boundary diffusion to be one-half of that for volume diffusion.
Take T=500°C; Qv=2 eV; (f0)v= 6* 10^15 (1/s) and (f0)g=1.5 10^11 (1/s).
Answer: 83
Problem: Calculate the approximate time (hrs) that is needed for diffusing carbon into steel to a depth of 1 mm when the diffusion coefficient at the temperature of heat treatment is 2*10^-7 cm2/s.
Answer: 3.47
Problem: Carbon atoms can best be interstitially accommodated in FCC  γ-iron by occupying the site halfway between two nearest corner atoms. Calculate the size (Å) of this open interstitial site (for carbon radius) by knowing that the radius of a  γ-iron atom is 1.29 Å. Now, the radius of a carbon atom is 0.71 Å.
Answer: 0.534
Problem: Calculate the electromotive force (V) from a silver half-cell whose electrolyte contains 1 g of Ag+ in 1 dm^3 of water.
Answer: 0.68
Problem: How much material (in g) is electrochemically removed from a copper electrode when a current of 5 A flows for 0.5 h through an appropriate electrochemical half-cell?
Answer: 2.96
Problem: Calculate the number of free electrons per cubic centimeter for sodium from resistance data ( ρ= 4.2 ∙ 10^(-8) Ω/m; relaxation time 3.1 ∙ 10^(-14) s.)
Answer: 2.73*10^22
Problem: What current (A) flows through a p–n diode to which a voltage of 0.3 V is applied and a saturation current of 1 μA is assumed at 300 K?
Answer: 0.11
Problem: Calculate the mobility of electrons (m2/V∙s) in a metal when the time between two electron/atom collisions is 2.5 * 10^(-12) s.
Answer: 0.44
Problem: Calculate the Curie constant for a paramagnetic material that was inserted at room temperature (300 K) in a magnetic field of 1.2 x 10^4 A/m and whose magnetic induction was measured to be 0.05 T. Assume that θ=0.
Answer: 694
Problem: A piece of platinum is inserted into a magnetic field that has a magnetic field strength of 10^3 [Oe]. Calculate the magnetic induction (T) in the material.
(χPt=264.4 x 10^-6 mks units.)
Answer: 0.1
Problem: The intensity of Na light passing through a gold film was measured to be about 15% of the incoming light. What is the thickness (nm) of the gold film? ( λ = 589 nm; k =3.2)
Answer: 27.8
Problem: The plasma frequency, ν1, can be calculated for the alkali metals by assuming one free electron per atom, i.e., by substituting Nf by the number of atoms per unit volume. Calculate ν1 (s^-1) for potassium.
Answer: 1.05 x 10^15
Problem: A block of copper whose mass is 100 g is quenched directly from an annealing furnace into a 200-g glass container that holds 500 g of water. What is the temperature of the furnace (K) if the water temperature rises from 0 to 15 ℃? (cglass = 0.5 J/g∙K)
Answer: 1142
Problem: Calculate the rate of heat loss (J/s∙m^2)in a 5-mm-thick window glass when the exterior temperature is 0  ℃ and the room temperature is 20  ℃.
Answer: 3.8   x 10^3