(A) According to Einstein's photoelectric equation: $h\nu = h\nu_{0} + K_{\text{max}}$,where $K_{\text{max}} = \frac{1}{2}mv^{2}$.Case $1$: When $\nu

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(A) According to Einstein's photoelectric equation: $h\nu = h\nu_{0} + K_{\text{max}}$,where $K_{\text{max}} = \frac{1}{2}mv^{2}$.Case $1$: When $\nu = 2\nu_{0}$:$h(2\nu_{0}) = h\nu_{0} + \frac{1}{2}mv_{1}^{2}$$h\nu_{0} = \frac{1}{2}mv_{1}^{2} \dots(1)$Case $2$: When $\nu = 5\nu_{0}$:$h(5\nu_{0}) = h\nu_{0} + \frac{1}{2}mv_{2}^{2}$$4h\nu_{0} = \frac{1}{2}mv_{2}^{2} \dots(2)$Dividing equation $(2)$ by $(1)$:$\frac{4h\nu_{0}}{h\nu_{0}} = \frac{\frac{1}{2}mv_{2}^{2}}{\frac{1}{2}mv_{1}^{2}}$$4 = \left(\frac{v_{2}}{v_{1}}\right)^{2}$$\frac{v_{2}}{v_{1}} = \sqrt{4} = 2$$v_{2} = 2v_{1}$Given $v_{2} = xv_{1}$,therefore $x = 2$.

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

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When light of frequency twice the threshold frequency is incident on a metal plate,the maximum velocity of the emitted electron is $v_{1}$. When the frequency of incident radiation is increased to five times the threshold value,the maximum velocity of the emitted electron becomes $v_{2}$. If $v_{2} = x v_{1}$,the value of $x$ will be...........

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A
$2$
B
$4$
C
$8$
D
$16$

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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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$A$ metal is exposed to light of wavelength $800 \, nm$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of the photoelectrons doubles when light of wavelength $500 \, nm$ is used. The work function of the metal is $... \, eV$ (Take $hc = 1230 \, eV \cdot nm$).

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$A$ photon of energy $8\,eV$ is incident on a metal surface of threshold frequency $1.6 \times 10^{15}\,Hz$. The maximum kinetic energy of photoelectrons emitted is .......... $eV$.
(Take $h = 6.6 \times 10^{-34}\,J\cdot s$; $1\,eV = 1.6 \times 10^{-19}\,J$)

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Sodium and copper have work functions of $2.3 \ eV$ and $4.5 \ eV$ respectively. The ratio of their threshold wavelengths is approximately .......

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If the threshold wavelength for sodium is $5420 \mathring{A}$,then the work function of sodium is ............ $eV$.

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In a photocell,the incident wavelength is $\lambda$. The maximum speed of the emitted photoelectrons is $u$. If the incident wavelength is changed to $3\lambda / 4$,then the maximum speed of the emitted photoelectrons will be:

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$A$ metal is exposed to light of wavelength $800 \, nm$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of the photoelectrons doubles when light of wavelength $500 \, nm$ is used. The work function of the metal is $... \, eV$ (Take $hc = 1230 \, eV \cdot nm$).

$A$ photon of energy $8\,eV$ is incident on a metal surface of threshold frequency $1.6 \times 10^{15}\,Hz$. The maximum kinetic energy of photoelectrons emitted is .......... $eV$.(Take $h = 6.6 \times 10^{-34}\,J\cdot s$; $1\,eV = 1.6 \times 10^{-19}\,J$)

Sodium and copper have work functions of $2.3 \ eV$ and $4.5 \ eV$ respectively. The ratio of their threshold wavelengths is approximately .......

If the threshold wavelength for sodium is $5420 \mathring{A}$,then the work function of sodium is ............ $eV$.

In a photocell,the incident wavelength is $\lambda$. The maximum speed of the emitted photoelectrons is $u$. If the incident wavelength is changed to $3\lambda / 4$,then the maximum speed of the emitted photoelectrons will be:

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$A$ photon of energy $8\,eV$ is incident on a metal surface of threshold frequency $1.6 \times 10^{15}\,Hz$. The maximum kinetic energy of photoelectrons emitted is .......... $eV$.
(Take $h = 6.6 \times 10^{-34}\,J\cdot s$; $1\,eV = 1.6 \times 10^{-19}\,J$)