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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3as050

Compare the electron in the $n = 2$ orbit of $He X^{+}$ with the electron in the $n = 1$ orbit of $H$ according to the Bohr model. Select all correct statements.

AThe orbit radius is twice as large
BThe orbital speed is twice as large
CThe time for one revolution is twice as long
DThe total energies are equal

Answer: A, C, D

r is proportional to

n^{2} / Z

: ratio = (4/2)/1 = 2. v is proportional to Z/n: ratio = (2/2)/1 = 1, so speed is the same. T = 2 pi r/v is proportional to

n^{3} / Z^{2}

: ratio = (8/4)/1 = 2. E is proportional to

Z^{2} / n^{2}

: (4/4) = 1, so the energies are equal.

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