Consider two hydrogen atoms H_A and H_B in ground state. Assume that hydrogen atom H_A is at rest and hydrogen atom H_B is moving with a speed and make head-on collision with the stationary hydrogen atom H_A. After the collision, both of them move together. What is minimum value of the kinetic energy of the moving hydrogen atom H_B, such that any one of the hydrogen atoms reaches first excitation state.

(a) A hydrogen atom is excited by radiation of wavelength 97.5 nm. Find the principal quantum number of the excited state
(b) Show that the total number of lines in emission spectrum is \(\frac { n(n-1) }{ 2 } \) Compute the total number of possible lines in emission spectrum as given in(a).

Calculate the mass defect and the binding energy per nucleon of the \(_{ 47 }^{ 108 }{ Ag }\) nucleus. [atomic mass of Ag = 107.905949]

On your birthday, you measure the activity of the sample ²¹⁰Bi which has a half-life of 5.01 days. The initial activity that you measure is 1µCi.
(a) What is the approximate activity of the sample on your next birthday? Calculate
(b) the decay constant
(c) the mean life
(d) initial number of atoms.

Assuming that energy released by the fission of a single  \(_{ 92 }^{ 235 }{ U }\) nucleus is 200MeV, calculate the number of fissions per second required to produce 1-watt power.