An electron in a hydrogen atom makes a transition from n = n₁ to n = n₂. The time period of electron in the final state is one-eighth to that in the initial state. Then which of the following statement is true?

Light of intensity 10¹² photons/s-m² of energy 6 eV per photon start falling at time t = 0, on a plate having work function of 2.5 eV and area 2 × 10^-4 m². If for every 10⁵ photons, one photoelectron is emitted, find the charge on the plate after 25 s.

A nuclei of a radioactive element is produced at constant rate α and simultaneously decays with decay constant λ. If at t = 0, number of nuclei is zero than find the number of nuclei at time t.

A sample of radioactive substance (half life = 20 sec) has 10⁶ nuclei at t = 0. Find the number of nuclei left in the sample at t = 10 sec.

If λ₁, λ₂ and λ₃ are the wavelengths of K_α X-rays emitted by three isotopes of mass number 113, 115 and 117 respectively, then

Which of these nuclear reactions is feasible?

Statement - 1 : If the accelerating potential in an X - ray tube is increased, the wavelengths of the characteristic X - rays do not change.

Statement - 2 : When an electron beam strikes the target in an X - ray tube, part of the kinetic energy is converted into X - ray energy.

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Find the number of electrons released