# Numerical Problems : Atomic Structures

#### Level – 1

1. Calculate the longest wavelength in the Paschen series of He+ ion.

2. Calculate the ratio of the wavelength of first and the ultimate line of Balmer series of Li2+ .

3 Calculate the number of photons emitted in 10 hours by a 60 W sodium lamp (λ = 5893 A °).

4. An electron collides with a hydrogen atom in its ground state and excited it to a state of n = 3. How much energy was given to the hydrogen atom in this inelastic collision ?

5. Hydrogen atom in states of high quantum number have been created in the laboratory and observed in space.

a) find the quantum number of the Bohr orbit in a H-atom whose radius is 0.0100 mm ?

b) what is the energy of H-atom in this state?

6. With what velocity should an α-particle travel towards the nucleus of a copper atom so as to arrive at a distance 10-13 metre from the nucleus of the copper atom.

7. An electron beam can undergo diffraction by crystals. Through what potential should a beam of electrons be accelerated. So that its wave length becomes equal to 1.54 A ° .

8. If the uncertainty in position and momentum are equal. Calculate the uncertainty in velocity for an electron.

9. Calculate the kinetic energy of an electron emitted from the surface of a metal by light of wavelength 5.5 x 10-8 cm. Threshold energy for the metal is 2.62 x 10-9 ergs.

10. Suppose 10-17J of energy is needed by the interior of human eye to see an object. How many photons of green light (λ = 550 nm) are needed to generate this minimum amount of energy?

## LEVEL – II

1. The power output for a certain laser transition was found to be 2.79 watt per square meter.
Given λ = 520 nm, calculate the number of quanta emitted per square meter per second.

2. An electron in a hydrogen like atom is in an excited state. It has a total energy of -3.4 eV. Calculate (i) kinetic energy and (ii) de-Broglie wavelength of the electron.

3. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photo electrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV. Find
a) The energy of the photons causing the photo electric emission?
b) The quantum numbers of the two levels involved in the emission of these photons?

4. Find the threshold wavelengths for photoelectric effect from a copper surface, a sodium surface and a caesium surface? The work function of these metals are 4.5 eV, 2.3 eV and 1.9 eV respectively.

5. Calculate (a) The de-Broglie wavelength of an electron moving with a velocity of 5.0 x 105 ms-1 and (b) Relative de-Broglie wavelength of an atom of Helium and an atom of oxygen moving with same velocity (h = 6.63 x 10-34 kg m2 sec-1).

6. The series limit for the Paschen series of hydrogen spectrum occurs at 8205.8 A °
Calculate.
a) Ionization energy of hydrogen atom
b) Wave length of the photon that would remove the electron in the ground state of the hydrogen atom.

7. The angular momentum of an electron in a particular orbit of Li2+ ion is 5.2728 x 10-34 kg m2/sec. Calculate the frequency of the spectral line when electron falls from this level to the level where angular momentum of electron will be 3.1636 x 10-34 kg – m2/sec.

8. The electron energy in hydrogen atom is given by E = 21.7 x 10-12/ n2 ergs. Calculate the energy required to remove an electron completely from n = 2 orbit. What is the longest wavelength (in cm) of light that can be used to cause this transition?

9. The wavelength corresponding to a transition when electron falls from a certain quantum level to the ground state of an He+ ion is 24.31 nm. Find the ratio of velocity of the electron in the next quantum level to that of velocity of light?

10. Calculate the energy emitted when electron of 1.0 g atom of hydrogen undergo transition giving the spectral lines of lowest energy in u.v. region of its atomic spectrum. (RH = 1.1 x 107 m-1, c = 3 x 108ms-1, h = 6.62 x 10-34 J – sec )