The Day the Earth Stopped

The film centers on Josh Myron (C. Thomas Howell) as six hundred and sixty six gigantic interplanetary robots land on Earth.
As the robots are landing, two humanoids arrive, one male and one female (Sinead McCafferty). Both are eventually captured by the military who tries to communicate with them. Eventually, the female starts talking to Myron and reveals that she can read his mind along with others. Myron is told that the entire human race is a threat to the rest of the galaxy and unless she is shown the value of humanity by sunset, the planet will be destroyed.
Attempts to communicate with the robots fail as they vaporize anyone that tries to attack them or even fires a rifle to get their attention. An effort is made to destroy the robots using Sidewinder Missiles, delivered by YF-22s. The missiles are ineffective and the attacking planes are destroyed by laser attack.
The woman, who reveals that her name in its closest English translation is Skye, also displays the ability to harness surrounding energy to protect herself. However, after using that, the military officer in charge of the "mission" starts to use a Taser on Skye, forcing Myron to intervene and be thrown off the project. He goes AWOL and as he is driving away, he is contacted by Skye telepathically and he returns to rescue her. The effort proves successful and starts a city-wide search for him and Skye.
The male also manages to escape as the robots begin a systemic attack on the planet, first with an EMP (which aids in Josh rescuing Skye). It's also discovered that the robots are slowing down the Earth's core and stopping the planet's rotation.
An effort is made to destroy one of the robots with a nuclear explosion, sacrificing 9000 inhabitants of a small island. When the bomb goes off, the machine emerges unharmed and Skye feels the pain of the people dying and almost passes out. Josh takes the time to comfort Skye before the military finds them again. Myron and Skye come across a married couple and have to put the wife in the back of a 4x4, as she is in labour. The husband delivers the child but is unaware of a complication until he realizes that his wife has stopped breathing. Myron hands the infant to Skye and tells her that if she wants to know the value of humanity, "you're staring at it". Myron and the husband desperately try to revive the wife but are unsuccessful. Myron realizes that the wife is dead and stops applying CPR. Skye, despite her earlier statement that she would not get involved, changes her mind and uses her powers to resurrect the wife.
Skye, now convinced of the value of humanity, needs to get to the closest robot to return home and end the invasion. Before they can get to the robot, Skye is shot by the military. Both are taken back to the base where Skye is treated for the injury as the planet's rotation stops and a major global earthquake hits.
The commander realizes, finally, that Myron was telling the truth and helps Myron move Skye to a vehicle. As they leave, they are chased by the psychologist, who is convinced that keeping Skye will prevent the robots from attacking further.
At the feet of the robot, Myron is shot by the psychologist; the robot, reacting to a perceived threat, vaporizes him. The robot man arrives, sees both Skye and Myron possibly dead and uses his own powers to revive both. Skye, in gratitude, hugs Myron before both the unnamed man and Skye are beamed aboard. The invasion ends and the robots depart the planet leaving behind major damage (such as half of the Eiffel Tower being destroyed), but the planet intact.

Question: What kind of explosion is used?
Answer: Nuclear