The ratio of the radius of the first orbit in | vedclass

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(A) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by the formula $r_n = \frac{n^2 h^2}{4 \pi^2 m Z e^2 k}$,where $m$ is the mas

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$1 : 1$

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(A) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by the formula $r_n = \frac{n^2 h^2}{4 \pi^2 m Z e^2 k}$,where $m$ is the mass of the electron.Since both hydrogen and deuterium have the same atomic number $(Z = 1)$ and the same electron mass $(m)$,the radius of the first orbit is independent of the mass of the nucleus.Therefore,the radius of the first orbit in hydrogen $(r_H)$ and deuterium $(r_D)$ are equal.The ratio $r_H : r_D$ is $1 : 1$.

The ratio of the radius of the first orbit in hydrogen to the radius of the first orbit in deuterium is .......

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