Question

The de-Broglie wavelength for an electron ray beam of 100 eV kinetic energy, if m= 9.1x10 - gin will
(a) 1.20 A
(b) 1.23 A
(C) 1.18 A
(d) 1.21 A

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Answer 1

answer : option (b) 1.23 A°

kinetic energy of an electron beam , E = 100eV

= 100 × 1.6 × 10^-19 Joule

= 1.6 × 10^-17 Joule

we know, relation between kinetic energy and linear momentum.

i.e., E = P²/2m

so, P = √{2Em}

now, De-broglie's wavelength = h/P

= h/√{2Em}

= 6.64 × 10^-34/√{2 × 1.6 × 10^-17 × 9.1 × 10^-31}

= 6.64 × 10^-34/(5.4 × 10^-24 )

= 1.2296 × 10^-10

= 1.23 A°

hence option (b) is correct choice.