1.

Determine the value of thede Broglie wavelength associated with the electron orbiting in the ground state of hydrogen atom ( Given E n = - (13.6)eV and Bohr radius r_(0) = 0.53Å). How will the de Broglie wavelength change when it is the first excited state?

Answer»

Solution :In ground state, the kinetic energy of the electron is
`K = -E = ( + 13.6eV)/( 1^(2)) = 13.6 xx 1.6 xx 10^(-19) J`
DE Broglie wavelength,
`lambda = ( h )/( p ) = ( h )/( sqrt(2mK))`
`lambda_(1)= ( 6.63 xx 10^(-34))/(sqrt( 2 xx 9.1 xx 10^(-31) xx 2.18 xx 10^(-18)))`
`= 9.33 xx 10^(-9)= 0.33nm`
Kinetic energy in the FIRST EXCITED state ( n = 2 )
`K = - E = + ( 13.6)/( 2^(2)) eV = + 3.4 eV`
`= 3.4 xx 1.6 xx 10^(-19) J`
`= 0.54 xx 10^(-18) J`
de Broglie wavelength,
`lambda_(2) = ( h)/( sqrt(2mK))`
`= ( 6.63 xx 10^(-34))/( sqrt( 2 xx 9.1 xx 10^(-31) xx 0.544 xx 10^(-15)))`
`= 2 xx 0.33 nm =0.66nm`


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