devarshi-dt-logo

Question:

Answer the following by appropriately matching the lists based on the information given in the paragraph. Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n. List-I List-II (i) Radius of the nth orbit (P) ∝ n⁻² (ii) Angular momentum of the electron in the nth orbit (Q) ∝ n⁻¹ (iii) Kinetic energy of the electron in the nth orbit (R) ∝ n⁰ (IV) Potential energy of the electron in the nth (S) ∝ n¹ (T) ∝ n² (U) ∝ n¹/² Which of the following has the correct combination considering List-I and List-II?

(II),(R)

(II),(Q)

(I),(P)

(I),(T)

Solution:

Correct option is D. (I),(T)
The kinetic energy of the electron in the nth orbit is given as:
K.E. = me⁴ / 8ε₀²n²h²
∴ K.E. ∝ n⁻²
Similarly, radius of nth orbit r ∝ n²Z
Angular momentum |L| ∝ n
and Potential energy P.E. ∝ -Z²/n²