Question

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Part A) When monochromatic UV light of wavelength 347 nm is sent through a diffraction grating,...

Part A) When monochromatic UV light of wavelength 347 nm is sent through a diffraction grating, the first order maximum occurs at 17.9o. How many lines per cm are in the grating?

Part B) Through what voltage should an electron be accelerated from rest so that it would produce the same interference pattern as this light.

Please answer both parts and show work.

Solutions

Expert Solution

Part A)

The number of lines per cm in the grating can be determined as follows.

Wavelength of the light is

The angle of the first order maximum is

The condition for maximum of interference pattern is,

      

Here, d is the slit spacing, m is the order of the pattern, and is wavelength.

Rearrange the equation for d.

    

    

Therefore, the number of lines per cm in the grating is,

     

Part B)

The voltage through which voltage electron be accelerated to get same interference pattern can be determined as follows.

The energy of the light of wavelength is,

         

The energy of the electron in terms of voltage is,

Here, e is the charge, V0 is the potential difference, h is the plank's constant, c is the speed of light, and is wavelength.

Rearrange the equation for V0 .

Therefore, the voltage is 3.6 V.

genius_generous answered 1 month ago
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