(B) The electronic configuration of $Li$ $(Z=3)$ is $1s^2 2s^1$. The third electron enters the $2s$ orbital,so $n = 2$.Angular momentum is given by $m

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Angular momentum = $\frac{h}{\pi}$,Energy = $\frac{-9\pi^2 e^4 m}{2h^2}$

(B) The electronic configuration of $Li$ $(Z=3)$ is $1s^2 2s^1$. The third electron enters the $2s$ orbital,so $n = 2$.Angular momentum is given by $mvr = \frac{nh}{2\pi}$. For $n=2$,Angular momentum = $\frac{2h}{2\pi} = \frac{h}{\pi}$.The energy of an electron in a hydrogen-like species is given by $E_n = \frac{-2\pi^2 m e^4 Z^2}{n^2 h^2}$.Substituting $Z=3$ and $n=2$: $E = \frac{-2\pi^2 m e^4 (3)^2}{(2)^2 h^2} = \frac{-2\pi^2 m e^4 (9)}{4 h^2} = \frac{-9\pi^2 m e^4}{2h^2}$.

Class 11 Chemistry Structure of Atom Atomic models and Planck's quantum theory

Medium

For a lithium atom,what can be said about the angular momentum and energy values for the permitted orbit of its third electron?

A
Angular momentum = $\frac{h}{2\pi}$,Energy = $\frac{-6\pi^2 e^4 m}{3h^2}$
B
Angular momentum = $\frac{h}{\pi}$,Energy = $\frac{-9\pi^2 e^4 m}{2h^2}$
C
Angular momentum = $\frac{h}{2\pi}$,Energy = $\frac{+3\pi^2 m e^4}{2h^2}$
D
Angular momentum = $\frac{3h}{2\pi}$,Energy = $\frac{+3\pi^2 m e^4}{4h^2}$

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Structure of Atom

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Atomic models and Planck's quantum theory

Which of the following is correct regarding Bohr's theory?

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The work functions (in $eV$) of $Mg, Cu, Ag, Na$ respectively are $3.7, 4.8, 4.3, 2.3$. From how many metals,the electrons will be ejected if their surfaces are irradiated with an electromagnetic radiation of wavelength $300 \ nm$ ?
$(h=6.6 \times 10^{-34} \ Js, 1 \ eV=1.6 \times 10^{-19} \ J)$

MediumAP EAMCET 2025

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$A$ source of monochromatic radiation of wavelength $400 \, nm$ provides $1000 \, J$ of energy in $10 \, seconds$. When this radiation falls on the surface of sodium,$x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \, nm$ is sufficient for ejection of electrons from the surface of sodium metal. The value of $x$ is $......$. (Nearest integer) $(h = 6.626 \times 10^{-34} \, Js)$

DifficultJEE MAIN 2021

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The frequency of the limiting line of the Lyman series in the hydrogen spectrum is ....

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What is the number of photons of light with a wavelength of $4000 \ pm$ that provide $1 \ J$ of energy?

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For a lithium atom,what can be said about the angular momentum and energy values for the permitted orbit of its third electron?

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Which of the following is correct regarding Bohr's theory?

The work functions (in $eV$) of $Mg, Cu, Ag, Na$ respectively are $3.7, 4.8, 4.3, 2.3$. From how many metals,the electrons will be ejected if their surfaces are irradiated with an electromagnetic radiation of wavelength $300 \ nm$ ?$(h=6.6 \times 10^{-34} \ Js, 1 \ eV=1.6 \times 10^{-19} \ J)$

The frequency of the limiting line of the Lyman series in the hydrogen spectrum is ....

What is the number of photons of light with a wavelength of $4000 \ pm$ that provide $1 \ J$ of energy?

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The work functions (in $eV$) of $Mg, Cu, Ag, Na$ respectively are $3.7, 4.8, 4.3, 2.3$. From how many metals,the electrons will be ejected if their surfaces are irradiated with an electromagnetic radiation of wavelength $300 \ nm$ ?
$(h=6.6 \times 10^{-34} \ Js, 1 \ eV=1.6 \times 10^{-19} \ J)$