(B) According to Einstein's photoelectric equation: $h\nu = h\nu_{0} + eV_{0}$, where $\nu_{0}$ is the threshold frequency.For the first case:$h\nu =

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(B) According to Einstein's photoelectric equation: $h\nu = h\nu_{0} + eV_{0}$, where $\nu_{0}$ is the threshold frequency.For the first case:$h\nu = h\nu_{0} + eV_{0}$ --- $(i)$For the second case:$h(\frac{\nu}{2}) = h\nu_{0} + e(\frac{V_{0}}{4})$ --- (ii)From equation $(i)$, we have $eV_{0} = h\nu - h\nu_{0}$.Substitute this into equation (ii):$\frac{h\nu}{2} = h\nu_{0} + \frac{1}{4}(h\nu - h\nu_{0})$Multiply the entire equation by $4$ to clear the denominator:$2h\nu = 4h\nu_{0} + h\nu - h\nu_{0}$$2h\nu = 3h\nu_{0} + h\nu$$h\nu = 3h\nu_{0}$$\nu_{0} = \frac{\nu}{3}$

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

Easy

When a certain metal surface is illuminated with light of frequency $v$, the stopping potential for photoelectric current is $V_{0}$. When the same surface is illuminated by light of frequency $\frac{v}{2}$, the stopping potential is $\frac{V_{0}}{4}$. The threshold frequency for photoelectric emission is:

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A
$\frac{v}{6}$
B
$\frac{v}{3}$
C
$\frac{2v}{3}$
D
$\frac{4v}{3}$

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Class 12 Questions

Class 12

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Chapter

Dual Nature of Radiation and matter

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Einstein's Photoelectric Equation and Energy Quantum of Radiation

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Radiation of wavelength $300 \ nm$ and intensity $100 \ W \ m^{-2}$ falls on the surface of a photosensitive material. If $2 \%$ of the incident photons produce photoelectrons,the number of photoelectrons emitted from an area of $2 \ cm^2$ of the surface per second is nearly:

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If in a photoelectric cell,the wavelength of incident light is changed from $4000 \mathring A$ to $3000 \mathring A$,then the change in stopping potential will be ..... $V$.

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The figure represents a graph of the maximum kinetic energy $(K)$ of photoelectrons (in $eV$) versus the frequency $(\nu)$ of incident radiation for a metal used as a cathode in a photoelectric experiment. The work function of the metal is ............. $eV$.

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The retarding potential necessary to stop the emission of photoelectrons,when a target material of work function $1.24 eV$ is irradiated with light of wavelength $4.36 \times 10^{-7} m$ is (in $eV$)

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The maximum velocity of an electron emitted by light of wavelength $\lambda$ incident on the surface of a metal of work function $\phi$ is:
Where $h =$ Planck's constant, $m =$ mass of electron, and $c =$ speed of light.

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Radiation of wavelength $300 \ nm$ and intensity $100 \ W \ m^{-2}$ falls on the surface of a photosensitive material. If $2 \%$ of the incident photons produce photoelectrons,the number of photoelectrons emitted from an area of $2 \ cm^2$ of the surface per second is nearly:

If in a photoelectric cell,the wavelength of incident light is changed from $4000 \mathring A$ to $3000 \mathring A$,then the change in stopping potential will be ..... $V$.

The figure represents a graph of the maximum kinetic energy $(K)$ of photoelectrons (in $eV$) versus the frequency $(\nu)$ of incident radiation for a metal used as a cathode in a photoelectric experiment. The work function of the metal is ............. $eV$.

The retarding potential necessary to stop the emission of photoelectrons,when a target material of work function $1.24 eV$ is irradiated with light of wavelength $4.36 \times 10^{-7} m$ is (in $eV$)

The maximum velocity of an electron emitted by light of wavelength $\lambda$ incident on the surface of a metal of work function $\phi$ is:Where $h =$ Planck's constant, $m =$ mass of electron, and $c =$ speed of light.

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The maximum velocity of an electron emitted by light of wavelength $\lambda$ incident on the surface of a metal of work function $\phi$ is:
Where $h =$ Planck's constant, $m =$ mass of electron, and $c =$ speed of light.