An electron is accelerated through a potential difference of 81V. What is the de Broglie wavelength associated with it? To which part of electromagnetic spectrum does this wavelength corresspond ?

Explanation

An electron is accelerated through potential difference `V =81 V`
de Broglie wavelength associated with `V lambda = ?`
`lambda = ( h )/( sqrt( 2 mE )) = ( h )/( sqrt( 2 m qV))`
For electron,
`lambda_(e ) = ( h ) /( sqrt( 2m_(e ) .e. V))`
`= ( 6.6 xx 10^(-24))/( sqrt( 2 xx 9.1 xx 10^(-31) xx 1.6 xx 10^(-19) xx81 ))`
`= ( 6.6 xx 10^(-34))/( sqrt( 2358 xx 10^(-50)))`
`= ( 6.6 xx 10^(-34))/( 48.57 xx 10^(-25) ) = 0.1358 xx 10^(-9)`
`= 1.36 xx 10^(-10) m `( or) ` 1.36 Å`
The electromagnetic spectrum associated with it.