Atomic Physics

Potential energy in hydrogen atom:

For Paschen series: transition to Minimum energy photon in Paschen series corresponds to But for the FIRST line in Paschen, use: Therefore, maximum energy of photon = 1.54 eV. So, work function must be less than or equal to 1.54 eV.

Ground state energy =
Second excited state

Positron is the antiparticle of an electron, having the same mass but a positive charge.

The magnetic moment of a revolving electron is related to its angular momentum by the expression: In Bohr’s atomic model, the angular momentum of the electron in the orbit is quantized as: Substituting into the magnetic moment equation: The term in parentheses is a constant called the Bohr magneton ( ). Thus: So, the magnetic moment is directly proportional to the principal quantum number . Hence, option (2) is correct.

For hydrogen atom, total energy and potential energy . Since the potential energy is half the total energy, we have .

In hydrogen spectrum:
Shortest wavelength in Lyman series:
Shortest wavelength in Balmer series:
Now subtract the second from the first:

So,
Take LCM and solve:

But this is the difference between and , and is , thus adjusting for the factor we get:

A photon is a quantum of electromagnetic radiation and it is known to have zero rest mass. Unlike protons, neutrons, and electrons which are massive particles, photons can travel at the speed of light precisely because they are massless.

Step 1: Understanding the Bohr Model and Energy Levels
In the Bohr model of the hydrogen atom, the energy of an electron in the -th orbit is given by: $ R_h n n_1 n_2 n_1 = 4 n_2 = 2 h c \lambda \Delta E = \frac{3R_h}{16} \lambda R_h = \frac{hc}{R} R \frac{16}{3R} \frac{8}{3R} \frac{3}{16R} \frac{3}{8R} $
Incorrect — incorrect numerator and denominator.

The energy levels of hydrogen atom are given by:


The energy difference between levels corresponds to the energy of emitted or absorbed photons.

- The first excited state energy (from to ) is:


This energy corresponds exactly to 10.2 eV, which is the energy of the first Lyman line (transition from ) in the ultraviolet region.

- Balmer lines correspond to transitions ending at level and have lower energies (< 10.2 eV).

Hence, excitation by 10.2 eV electrons causes the hydrogen atom to emit the first Lyman line.