SATHEE: Modern Physics 1 Question 49

Modern Physics 1 Question 49

45. Wavelengths belonging to Balmer series lying in the range of $450 n m$ to $750 n m$ were used to eject photoelectrons from a metal surface whose work function is $2.0 e V$ . Find (in eV) the maximum kinetic energy of the emitted photoelectrons. (Take $h c = 1242 e V n m$ .

$(2004, 4$ M)

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Solution:

Wavelengths corresponding to minimum wavelength $(λ_{min})$ or maximum energy will emit photoelectrons having maximum kinetic energy. $(λ_{min})$ belonging to Balmer series and lying in the given range $(450 n m$ to $750 n m$ ) corresponds to transition from $(n = 4$ to $n = 2)$ . Here,

$\begin{aligned} E_{4} = - \frac{13.6}{(4)^{2}} = - 0.85 e V \\ and \begin{aligned} E_{2} & = - \frac{13.6}{(2)^{2}} = - 3.4 e V \\ ∴ Δ E & = E_{4} - E_{2} = 2.55 e V \\ K_{max} & = Energy of photon - work function \\ = 2.55 - 2.0 = 0.55 e V \end{aligned} \end{aligned}$

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Modern Physics 1 Question 49

45. Wavelengths belonging to Balmer series lying in the range of 450nm to 750nm were used to eject photoelectrons from a metal surface whose work function is 2.0eV. Find (in eV) the maximum kinetic energy of the emitted photoelectrons. (Take hc=1242eVnm.

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45. Wavelengths belonging to Balmer series lying in the range of $450 n m$ to $750 n m$ were used to eject photoelectrons from a metal surface whose work function is $2.0 e V$ . Find (in eV) the maximum kinetic energy of the emitted photoelectrons. (Take $h c = 1242 e V n m$ .