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Exercise · Q1

Q.Choose the correct option.
The energy difference between the shells goes on ........... when moved away from the nucleus.

(a) Increasing
(b) decreasing
(c) equalizing
(d) static
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Step 1. Recall the Bohr energy formula. For hydrogen, the energy of the stationary state nn is En=−RH(1n2)E_n = -R_H\left(\frac{1}{n^2}\right) with RH=2.18×10−18R_H = 2.18\times10^{-18} J.

Step 2. Compute a few levels. E1=−2.18×10−18E_1 = -2.18\times10^{-18} J. E2=−2.18×10−18×14=−0.545×10−18E_2 = -2.18\times10^{-18}\times\frac{1}{4} = -0.545\times10^{-18} J. E3=−2.18×10−18×19≈−0.242×10−18E_3 = -2.18\times10^{-18}\times\frac{1}{9} \approx -0.242\times10^{-18} J.

Step 3. Compare successive gaps. Gap between n=1n=1 and n=2n=2: E2−E1=1.635×10−18E_2-E_1 = 1.635\times10^{-18} J. Gap between n=2n=2 and n=3n=3: E3−E2≈0.303×10−18E_3-E_2 \approx 0.303\times10^{-18} J — a much smaller gap.

Step 4. The gaps get smaller (not bigger) as you move to shells farther from the nucleus, because 1n2\frac{1}{n^2} flattens out for large nn.

✓Final answer

(b) decreasing

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