(A) The radius of the $n$-th orbit in Bohr's model is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}$. Since $r \propto 1/m$,if the mass $m$ is

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$E_0 = -27.2 \text{ eV}; r_0 = a_0/2$

(A) The radius of the $n$-th orbit in Bohr's model is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}$. Since $r \propto 1/m$,if the mass $m$ is doubled,the new radius $r_0$ becomes $r_0 = a_0/2$.The energy of the $n$-th orbit is given by $E_n = -\frac{m e^4}{8 \epsilon_0^2 n^2 h^2}$. Since $E \propto m$,if the mass $m$ is doubled,the new energy $E_0$ becomes $E_0 = 2 \times (-13.6 \text{ eV}) = -27.2 \text{ eV}$.Thus,the correct option is $A$.

Class 12 Physics Atoms Bohr's Model of Hydrogen Atom

Medium

In a hypothetical Bohr hydrogen atom,the mass of the electron is doubled. The energy $E_0$ and the radius $r_0$ of the first orbit will be ($a_0$ is the Bohr radius).

A
$E_0 = -27.2 \text{ eV}; r_0 = a_0/2$
B
$E_0 = -27.2 \text{ eV}; r_0 = a_0$
C
$E_0 = -13.6 \text{ eV}; r_0 = a_0/2$
D
$E_0 = -13.6 \text{ eV}; r_0 = a_0$

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Bohr's Model of Hydrogen Atom

When an electron jumps from the orbit $n=2$ to $n=4$,the wavelength of the radiation absorbed will be ($R$ is Rydberg's constant).

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EasyIIT 1997

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In a hydrogen-like atom,an electron makes a transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$. If $n >> 1$,the frequency of radiation emitted is proportional to:

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In a hypothetical Bohr hydrogen atom,the mass of the electron is doubled. The energy $E_0$ and the radius $r_0$ of the first orbit will be ($a_0$ is the Bohr radius).

Similar Questions

When an electron jumps from the orbit $n=2$ to $n=4$,the wavelength of the radiation absorbed will be ($R$ is Rydberg's constant).

The electron in a hydrogen atom makes a transition from the $M$ shell to the $L$ shell. The ratio of the magnitudes of the initial to the final centripetal acceleration of the electron is:

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

As per the Bohr model,the minimum energy (in $eV$) required to remove an electron from the ground state of a doubly ionized $Li$ atom $(Z = 3)$ is:

In a hydrogen-like atom,an electron makes a transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$. If $n >> 1$,the frequency of radiation emitted is proportional to:

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