HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q34 Solution: A small metal plate work function ) is kept at a distance from…

QPages 365-366: Q34: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q34 Solution: A small metal plate work function ) is kept at a distance from…

A small metal plate work function

\phi

) is kept at a distance

d

from a singly-ionised, fixed ion. A monochromatic light beam is incident on the metal plate and photoelectrons are emitted. Find the maximum wavelength of the light beam, so that some of the photoelectrons may go round the ion along a circle.

Step-by-Step Verified Solution

**Answer:**

\lambda_{max} = \frac{hc}{\phi + \frac{ke^2}{2d}}

. **Step-by-Step Explanation:** For the photoelectron to go round the ion in a circle, the electric force provides the centripetal force.

\frac{ke^2}{d^2} = \frac{mv^2}{d} \Rightarrow mv^2 = \frac{ke^2}{d}

KE = \frac{1}{2}mv^2 = \frac{ke^2}{2d}

. Energy equation:

\frac{hc}{\lambda} = \phi + KE = \phi + \frac{ke^2}{2d}

\lambda_{max} = \frac{hc}{\phi + \frac{ke^2}{2d}}

QPages 365-366: Q34: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q34 Solution: A small metal plate work function ) is kept at a distance from…

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