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An electron labeled e₁ is in the fifth energy level, while another electron labeled e₂ is in the fourth energy level. The orbital radius of e₁ is five times that of e₂. What is the ratio of the speed of e₁ (v₁) to the speed of e₂ (v₂)?

1. 5: 1
2. 4: 1
3. 1: 5
4. 1: 4

Correct answer: 1: 4

Solution

From r∝n^2/Z, r1/r2=(25/Z1)(Z2/16)=5 gives Z2/Z1=16/5. From v∝Z/n, v1/v2=(Z1/5)/(Z2/4)=(4/5)(Z1/Z2)=(4/5)(5/16)=1/4. So v1:v2=1:4 (option index 3).

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