A Hydrogen-like atom has atomic number Z. Photons emitted in the electronic transitions from level to level in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated

Question

A Hydrogen-like atom has atomic number Z. Photons emitted in the electronic transitions from level $n = 4$ to level $n = 3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is 1.95 eV. If the photoelectric threshold wavelength for the target metal is 310 nm, the value of Z is ______. [2023]

[Given: hc = 1240 eV–nm and Rhc = 13.6 eV, where R is the Rydberg constant, h is Planck's constant and c is the speed of light in vacuum.]

Smart Achievers · Accepted Answer

(3)

$K_{\max} = E - W$ $\Rightarrow E_{4 \to 3} = K_{\max} + W = 1.95 + \frac{h c}{λ}$

$= 1.95 + \frac{1240}{310} = 5.95 eV$

$13.6 Z^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = 5.95$

$13.6 Z^{2} (\frac{7}{9 \times 16}) = 5.95$

$\Rightarrow Z^{2} = \frac{5.95 \times 9 \times 16}{13.6 \times 7} = 9$

$∴$ $Z = 3$

Solution

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Solution

Ans. (3) Kmax=E-W⇒E4→3=Kmax+W=1.95+hcλ =1.95+1240310=5.95 eV 13.6Z2(132-142)=5.95 13.6Z2(79×16)=5.95 ⇒Z2=5.95×9×1613.6×7=9 ∴ Z=3

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