(D) According to Einstein's photoelectric equation,the maximum kinetic energy $K_{\max}$ of the emitted electron is given by: $K_{\max} = E - \phi$ wh

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$\left[\frac{2(hc-\phi \lambda)}{m \lambda}\right]^{\frac{1}{2}}$

(D) According to Einstein's photoelectric equation,the maximum kinetic energy $K_{\max}$ of the emitted electron is given by: $K_{\max} = E - \phi$ where $E = \frac{hc}{\lambda}$ is the energy of the incident photon. Substituting the values,we get: $\frac{1}{2} mv_{\max}^2 = \frac{hc}{\lambda} - \phi$ $\frac{1}{2} mv_{\max}^2 = \frac{hc - \phi \lambda}{\lambda}$ Multiplying both sides by $\frac{2}{m}$: $v_{\max}^2 = \frac{2(hc - \phi \lambda)}{m \lambda}$ Taking the square root on both sides: $v_{\max} = \sqrt{\frac{2(hc - \phi \lambda)}{m \lambda}}$ Thus,the correct option is $D$.

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

Medium

The light of wavelength $\lambda$ is incident on the surface of a metal with work function $\phi$ and emits electrons. What is the maximum velocity of the emitted electrons? [Given: $m=$ mass of electron,$h=$ Planck's constant,$c=$ velocity of light]

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A
$\left[\frac{2(hc-\lambda)}{m \lambda}\right]^{\frac{1}{2}}$
B
$\left[\frac{2(hc-\phi) \lambda}{mc}\right]^{\frac{1}{2}}$
C
$\left[\frac{2(hc-\lambda)}{m \lambda}\right]$
D
$\left[\frac{2(hc-\phi \lambda)}{m \lambda}\right]^{\frac{1}{2}}$

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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 light of wavelength $\lambda$ is incident on the surface of a metal with work function $\phi$ and emits electrons. What is the maximum velocity of the emitted electrons? [Given: $m=$ mass of electron,$h=$ Planck's constant,$c=$ velocity of light]

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When light of wavelength $\lambda$ is incident on a photosensitive surface,the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on the same surface,the stopping potential is $\frac{V}{6}$. Then the threshold wavelength for the surface is:

Light of wavelength $488 \, nm$ produced by an Argon laser is used in the photoelectric effect. When light from this spectral line is incident on the cathode, the stopping potential of the photoelectrons is $0.38 \, V$. The work function of the cathode material is (in $ \, eV$)

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