The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of photon with the most enegy ?

Options

A. III
B. IV
C. I
D. II

Answer

A

Explanation

As, E ` = Rhc[ ( 1 ) /( n _1^ 2 ) - ( 1 )/( n _ 2 ^ 2 ) ] `
` rArr E _("(" 4 to 3 ")") = Rhs [ ( 1 ) /( 3^ 2) - ( 1 )/( 4 ^ 2) ] `
` = Rhc[ ( 7 ) /( 9 xx 16 ) ] = 0.05Rhc `
` rArr E _ ("(" 4 to 2 ")") = Rhc [ ( 1 ) /( 2 ^ 2 ) - ( 1 ) /( 4^ 2 ) ] `
` = Rhc [ ( 3 ) /( 16) ] = 0.2 Rhc `
` rArr E _ ("(" 2 to 1 ")") = Rhc [ ( 1 ) /( ( 1) ^ 2) - ( 1 ) /( (2)^2) ]`
` = Rhc [ ( 3 ) /( 4) ] = 0.75 Rhc `
` rArr E _ ( "(" 1 to 3 ")") = Rhc [ ( 1 ) /((3) ^2) - (1) /( (1)^ 2 ) ] `
` = - ( 8 ) /(9) Rhc = -0.9 Rhc `
Thus, transition III gives most energy. Transition I represents the absorption of energy.