1. Tardigrade
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  4. The radiation corresponding to 3 arrow 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 1 0- 4 T . If the radius of the largest circular path followed by these electrons is 10 mm, the work function of the metal is close to :

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Q. The radiation corresponding to $3 \rightarrow 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 1 0^{- 4} T$ . If the radius of the largest circular path followed by these electrons is 10 mm, the work function of the metal is close to :

NTA AbhyasNTA Abhyas 2020

Solution:

We know that
$\text{r} = \frac{\text{m} \upsilon}{\text{Bq}}$
$∴ \, \, \, \upsilon = \frac{\text{Bqr}}{\text{m}}$
$∴ \, \, \, \text{KE} = \frac{1}{2} \text{m} \text{v}^{2}$
$= \frac{\text{B}^{2} \text{q}^{2} \text{R}^{2}}{2m}$
= 0.79 eV
Now from photoelectric equation
$\text{E} = \phi + \text{KE}$
$∴ \, \, \, \phi = \text{E} - \text{KE}$
$= \text{1.89} - \text{0.79}$
$= \text{1.1 eV}$