Integer Answer Type Questions for JEE: Atoms & Nuclei | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. The ionization potential of H-atom is 13.6 V. When it is excited from ground state by monochromatic radiations of 970.6 Å, the number of emission lines will be (according to Bohr's theory)

Ans. 6


⇒ n₂ = 4
∴ Number of emission lines

Q.2. An electron passing through a potential difference of 4.9 V collides with a mercury atom and transfers it to the first excited state. What is the wavelength of a photon corresponding to the transition of the mercury atom to its normal state?

Ans. 2525 Å

Q.3. In the nuclear fusion reaction,  given that the repulsive potential energy between the two nuclei is 7.7 × 10⁻¹⁴ J, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant k=1.38 × 10⁻²³J/K]

Ans. 10⁹K
Kinetic energy of the molecules of a gas at a temp.
T is 3/2 kT
To initiate the reaction 3/2 =7.7 × 10⁻¹⁴J
⇒ 3/2 × 1.38 × 10^-23 T = 7.7 × 10⁻¹⁴J
⇒ T = 3.7 × 10⁹K

Q.4. A nucleus with mass number 220 initially at rest emits an a-particle. If the Q value of the reaction is 5.5 Mel, calculate the kinetic energy of the α-particle

Ans. 5.4 MeV

Q-value of the reaction is 5.5 eV
i.e. k₁ + k₂= 5.5 MeV … (i)
By conservation of linear momentum
 .. (ii)
On solving equation (i) and (ii) we get k₂ = 5.4 MeV

Q.5. The half-life of radioactive Radon is 3.8 days. The time at the end of which 1/20th of the Radon sample will remain undecayed is (Given log₁₀ e = 0.4343)

Ans. 16.5
By the formula N = N₀e^-λt
Given,


Taking log of both sides


⇒ t = 16.5 days