(C) The work function $\phi$ of the metal is given by $\phi = h\nu$,where $\nu$ is the cutoff (threshold) frequency.According to Einstein's photoelect

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(C) The work function $\phi$ of the metal is given by $\phi = h\nu$,where $\nu$ is the cutoff (threshold) frequency.According to Einstein's photoelectric equation,the maximum kinetic energy $K_{\max}$ of the emitted electron is given by $K_{\max} = E - \phi$.Here,the incident frequency is $2\nu$,so the incident energy $E = h(2\nu) = 2h\nu$.Substituting the values,we get $K_{\max} = 2h\nu - h\nu = h\nu$.Since $K_{\max} = \frac{1}{2}mv_{\max}^2$,we have $\frac{1}{2}mv_{\max}^2 = h\nu$.Solving for $v_{\max}$,we get $v_{\max}^2 = \frac{2h\nu}{m}$,which implies $v_{\max} = \sqrt{\frac{2h\nu}{m}}$.

Class 12 Physics Dual Nature of Radiation and Matter Einstein's Photoelectric Equation and Energy Quantum of Radiation

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For photoelectric emission from a certain metal,the cutoff frequency is $\nu$. If radiation of frequency $2\nu$ impinges on the metal plate,the maximum possible velocity of the emitted electron will be ($m$ is the electron mass).

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A
$\sqrt{\frac{h\nu}{2m}}$
B
$\sqrt{\frac{h\nu}{m}}$
C
$\sqrt{\frac{2h\nu}{m}}$
D
$2\sqrt{\frac{h\nu}{m}}$

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Dual Nature of Radiation and Matter

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Einstein's Photoelectric Equation and Energy Quantum of Radiation

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Light of frequency $4\nu_0$ is incident on a metal surface with threshold frequency $\nu_0$. The maximum kinetic energy of the emitted photoelectrons is:

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When monochromatic light falls on a photo-sensitive metal,an electron is emitted with maximum velocity $1.6 \times 10^6 \ m/s$. Find the stopping potential.
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When a photosensitive surface is irradiated by light of wavelengths $\lambda_1$ and $\lambda_2$,the kinetic energies of the emitted photoelectrons are $E_1$ and $E_2$ respectively. The work function of the photosensitive surface is:

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$A$ metal surface is illuminated by light of two different wavelengths $248 \ nm$ and $310 \ nm$. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_1$ and $u_2$,respectively. If the ratio $u_1: u_2 = 2: 1$ and $hc = 1240 \ eV \ nm$,the work function of the metal is nearly: (in $eV$)

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For photoelectric emission from a certain metal,the cutoff frequency is $\nu$. If radiation of frequency $2\nu$ impinges on the metal plate,the maximum possible velocity of the emitted electron will be ($m$ is the electron mass).

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Light of frequency $4\nu_0$ is incident on a metal surface with threshold frequency $\nu_0$. The maximum kinetic energy of the emitted photoelectrons is:

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When monochromatic light falls on a photo-sensitive metal,an electron is emitted with maximum velocity $1.6 \times 10^6 \ m/s$. Find the stopping potential.
[charge of electron $= 1.6 \times 10^{-19} \ C$,mass of electron $= 9 \times 10^{-31} \ kg$] (in $V$)