NEET Atoms and Nuclei — Set 11

Question 1

In the Bohr model, what is the ratio of the kinetic energy of an electron in the $ n = 2 $ state to that in the $ n = 1 $ state?

Accepted Answer

$ K = \frac{e^2}{8\pi\epsilon_0 r} $, $ r_n \propto n^2 $. $ K_n \propto \frac{1}{n^2} $. Ratio = $ \frac{K_2}{K_1} = \frac{1/2^2}{1/1^2} = \frac{1}{4} $.

Question 2

What is the orbital period of an electron in the $ n = 3 $ orbit if $ v_1 = 2.2 \times 10^6 \, \text{m/s} $ and $ r_1 = 5.3 \times 10^{-11} \, \text{m} $?

Accepted Answer

$ v_3 = \frac{2.2 \times 10^6}{3} \approx 7.33 \times 10^5 \, \text{m/s} $. $ r_3 = 9 \times 5.3 \times 10^{-11} = 4.77 \times 10^{-10} \, \text{m} $. $ T = \frac{2\pi r_3}{v_3} = \frac{2 \times 3.14 \times 4.77 \times 10^{-10}}{7.33 \times 10^5} \approx 4.09 \times 10^{-15} \, \text{s} $.

Question 3

What is the energy difference between the $ n = 4 $ and $ n = 2 $ states in a hydrogen atom? (Use $ E_n = -\frac{13.6}{n^2} \, \text{eV} $)

Accepted Answer

$ E_4 = -0.85 \, \text{eV} $, $ E_2 = -3.4 \, \text{eV} $. $ \Delta E = -0.85 - (-3.4) = 2.55 \, \text{eV} $.

NEET Physics: Atoms and Nuclei — Practice Set 11

Q1. In the Bohr model, what is the ratio of the kinetic energy of an electron in the \( n = 2 \) state to that in the \( n = 1 \) state?

Q2. What is the orbital period of an electron in the \( n = 3 \) orbit if \( v_1 = 2.2 \times 10^6 \, \text{m/s} \) and \( r_1 = 5.3 \times 10^{-11} \, \text{m} \)?

Q3. What is the energy difference between the \( n = 4 \) and \( n = 2 \) states in a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q4. What is the speed of an electron in the \( n = 5 \) orbit of a hydrogen atom if its speed in \( n = 1 \) is \( 2.2 \times 10^6 \, \text{m/s} \)?

Q5. What is the kinetic energy of an electron in the \( n = 4 \) state of a hydrogen atom? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q6. In the Bohr model, how many de Broglie wavelengths fit into the circumference of the \( n = 5 \) orbit?

Q7. Which of the following statements is incorrect about Thomson’s model?

Q8. What does the absorption spectrum of a hydrogen atom reveal?

Q9. An electron in a hydrogen atom has a total energy of -3.4 eV. What is its kinetic energy?