Use a_0 = 0.529 AA and a first-orbit speed of 2.19x10^6 m s^-1 for hydrogen. An electron stays in the n=2 orbit for 1.0x10^-8 s before dropping to a lower level. How many revolutions does it complete, in units of 10^6 (two decimals)?

JEE Advanced levelNumerical answerDifficulty 3 of 3as100

Use $a_{0} = 0.529 \overset{˚}{A}$ and a first-orbit speed of $2.19 \times 1 0^{6} m s^{- 1}$ for hydrogen. An electron stays in the $n = 2$ orbit for $1.0 \times 1 0^{- 8} s$ before dropping to a lower level. How many revolutions does it complete, in units of $1 0^{6}$ (two decimals)?

Numerical answer type, answer in 1e6, tolerance 0.03.

r_{2} = 4 a_{0}

and

v_{2} = 2.19 \times 1 0^{6} /2 m s^{- 1}

, so

T = 2 π r_{2} / v_{2} = 1.214 e - 15 s

. Revolutions

= 1 0^{- 8} / T = 8.24 \times 1 0^{6}