Question 269: Dual Nature of Matter and Radiation

Question

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to that of copper is nearest to

Accepted Answer

Work functions:
Sodium: $\phi_{Na} = 2.3 \, 	ext{eV}$
Copper: $\phi_{Cu} = 4.5 \, 	ext{eV}$
Threshold wavelength is related to work function via:
$ \lambda = \frac{hc}{\phi} $
where $\phi$ is in energy units (eV), and $hc \approx 1240 \, 	ext{eVÃÂ·nm}$.
So:
$ \lambda_{Na} = \frac{1240}{2.3} \, 	ext{nm}, \quad \lambda_{Cu} = \frac{1240}{4.5} \, 	ext{nm} $
Now the ratio:
$ \frac{\lambda_{Na}}{\lambda_{Cu}} = \frac{1240/2.3}{1240/4.5} = \frac{4.5}{2.3} $
$ \frac{\lambda_{Na}}{\lambda_{Cu}} \approx 1.96 \approx 2 $
So the ratio of threshold wavelengths (Na : Cu) Ã¢ÂÂ
2 : 1
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Answer: Option D (2 : 1)

Answer

$1: 4$

Answer

$4: 1$

Answer

$1: 2$

Answer

$2: 1$

Dual Nature of Matter and Radiation

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. The ratio of threshold wavelength of sodium to that of copper is nearest to

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