1.

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which a neutron, would have the same the Broglie wavelength.

Answer»

Solution :GIVEN `:` `lambda = 589 nm = 5.89 xx 10^(-7) m`
The de Broglie wavelength `lambda - ( h )/( p )= ( h )/( sqrt( 2mE_(k))) `
`RARR lambda^(2) = ( h^(2))/(2mE_(k))`
Kinetic energy `E_(k )=( h^(2))/( 2mlambda^(2))`
For neutron `m = 1.67 xx 10^(-27) kg`
`E_(k)= ((6.63 xx 10^(-34))^(2))/( 2 xx 1.67 xx 10^(-31)xx ( 5.89 xx 10^(-7))^(2))`
`= 3.79 xx 10^(-28)J`


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