(D) According to Einstein's photoelectric equation,the maximum kinetic energy is given by $K_{\max} = E - W_0$,where $E$ is the energy of the incident

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(D) According to Einstein's photoelectric equation,the maximum kinetic energy is given by $K_{\max} = E - W_0$,where $E$ is the energy of the incident photon and $W_0$ is the work function.For the first case: $E_1 = 2h\nu_0$ and $W_0 = h\nu_0$.$\frac{1}{2}mv_1^2 = 2h\nu_0 - h\nu_0 = h\nu_0$ ... $(i)$For the second case: $E_2 = 5h\nu_0$ and $W_0 = h\nu_0$.$\frac{1}{2}mv_2^2 = 5h\nu_0 - h\nu_0 = 4h\nu_0$ ... $(ii)$Dividing equation $(ii)$ by $(i)$:$\frac{\frac{1}{2}mv_2^2}{\frac{1}{2}mv_1^2} = \frac{4h\nu_0}{h\nu_0}$$\left(\frac{v_2}{v_1}\right)^2 = 4$$\frac{v_2}{v_1} = 2$Given $v_1 = 4 \times 10^6 \, m/s$,we find:$v_2 = 2 \times v_1 = 2 \times (4 \times 10^6 \, m/s) = 8 \times 10^6 \, m/s$.

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

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$A$ photosensitive metallic surface has a work function $h\nu_0$. If photons of energy $2h\nu_0$ fall on this surface,the electrons are emitted with a maximum velocity of $4 \times 10^6 \, m/s$. When the photon energy is increased to $5h\nu_0$,the maximum velocity of the photoelectrons will be:

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A
$2 \times 10^6 \, m/s$
B
$2 \times 10^7 \, m/s$
C
$8 \times 10^5 \, m/s$
D
$8 \times 10^6 \, m/s$

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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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The threshold frequency of a photosensitive material is $v$. When photons of frequency $2v$ are incident on the material,photoelectrons are emitted with a maximum linear momentum $P$. To get photoelectrons with maximum linear momentum $2P$,the frequency of the incident photons is: (in $v$)

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$A$ photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\frac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the first case is one-third that in the second case,the work function of the surface of the material is ($c=$ speed of light,$h=$ Planck's constant).

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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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When a metal is irradiated by monochromatic light,the maximum kinetic energy of the photoelectrons is $1.2 \ eV.$ If the frequency of the light is increased by $50 \%$,then the maximum kinetic energy of the photoelectrons is $3.6 \ eV.$ Evaluate the work function of the metal.

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$A$ photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\lambda /2$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3$ times that in the first case,the work function of the surface of the material is
$(h =$ Planck's constant,$c =$ speed of light $)$

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$A$ photosensitive metallic surface has a work function $h\nu_0$. If photons of energy $2h\nu_0$ fall on this surface,the electrons are emitted with a maximum velocity of $4 \times 10^6 \, m/s$. When the photon energy is increased to $5h\nu_0$,the maximum velocity of the photoelectrons will be:

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The threshold frequency of a photosensitive material is $v$. When photons of frequency $2v$ are incident on the material,photoelectrons are emitted with a maximum linear momentum $P$. To get photoelectrons with maximum linear momentum $2P$,the frequency of the incident photons is: (in $v$)

$A$ 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 $h = 6.6 \times 10^{-34}\,J\cdot s$; $1\,eV = 1.6 \times 10^{-19}\,J$)

When a metal is irradiated by monochromatic light,the maximum kinetic energy of the photoelectrons is $1.2 \ eV.$ If the frequency of the light is increased by $50 \%$,then the maximum kinetic energy of the photoelectrons is $3.6 \ eV.$ Evaluate the work function of the metal.

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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 $h = 6.6 \times 10^{-34}\,J\cdot s$; $1\,eV = 1.6 \times 10^{-19}\,J$)