According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in the nth orbit and its radius in the nth orbit

Question

According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in the nth orbit and its radius in the nth orbit (A) is proportional to n2 (B) is inversely proportional to n3 (C) has a constant value of 10.2 eV - mathringA (D) has a constant value of 7.2 eV - mathringA

Tardigrade Admin · Accepted Answer

En propto (1/n2) and rn propto n2 Therefore, En rn is independent of n. Hence, E1 r1=(13.6 eV )(0.53 mathringA) =7.2 cV - mathringA= constant

Q. According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in the $n$ th orbit and its radius in the $n$ th orbit

is proportional to $n^{2}$

is inversely proportional to $n^{3}$

has a constant value of $10.2 e V - \overset{˚}{A}$

has a constant value of $7.2 e V - \overset{˚}{A}$

$E_{n} \propto \frac{1}{n ^{2}}$ and $r_{n} \propto n^{2}$
Therefore, $E_{n} r_{n}$ is independent of $n$ .
Hence, $E_{1} r_{1} = (13.6 e V) (0.53 \overset{˚}{A})$
$= 7.2 c V - \overset{˚}{A} =$ constant

Q. According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in the nth orbit and its radius in the nth orbit

is proportional to n2

is inversely proportional to n3

has a constant value of 10.2eV−A˚

has a constant value of 7.2eV−A˚