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A daredevil wishes to bungee-jump from a hot-air balloon 62.5 m above a carnival midway. He will use a piece of uniform elastic cord tied to a harness around his body to stop his fall at a point 13.0 m above the ground. Model his body as a particle and the cord as having negligible mass and a tension force described by Hooke's force law. In a preliminary test, hanging at rest from a 5.00-m length of the cord, the jumper finds that his body weight stretches it by 1.45 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon.

(a) What length of cord should he use?
m

(b) What maximum acceleration will he experience?
m/s2
If Nq electrons are contained in the volume at absolute zero temperature, describe how you would count the number of states/orbitals in the system.

 If Nq electrons are contained in the volume at absolute zero temperature, describe how you would count the number of states/orbitals in the system.


Using the separation of variables technique, derive the time-independent Schrodinger equation (T.I.S.E.) in three dimensions. 


 State the time-dependent Schrodinger equation in three dimensions. State the meaning of all the terms in the equation. 


A nuclear scientist claimed that he has accurately measured the energy and momentum of a
radiation (e.g. Alpha, Beta, Gamma-ray, Neutron etc.) using his most sensitive Geiger Muller
counter. Can you believe his claim is correct? If yes, give a proper justification for his claim and
if no, then also prove that he is wrong

Consider a one-dimensional infinite square well with N particles. Given that all particles occupy the ground state, calculate the total energy of the system. Now assume that each energy level can hold no more than two particles. Calculate the energy of the ground state of the system and the maximum particle energy called the Fermi energy. Find an expression for the density of states for the infinite square well.


derive the formula for the energy density of radiation inside an enclosed cavity
at constant temperature T using classical physics.Show how the classical theory is modified to correctly explain the energy density.
derive the formula for the energy density of radiation inside an enclosed cavity at constant temperature T using classical physics, show how the classical theory is modified.
How long do quantum fluctuations last for?
Like can they in theory, if a long enough period of time passed isnt it possible for, idk, a baseball to suddenly appear. I just want to know. If in theory quantum fluctuations can create matter from nothing and the matter staying in exsistance. Sorry if this question was worded a bit weird.
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