The mass of an electron is 9.1 × 10-31 kg. If its kinetic energy is 3.0 × 10-25 J, calculate its wavelength.

Kinetic energy. K.E. = ½ mv2 => v2 = (2 x K.E.) / mGiven, K.E. = 3 x 10-25 J = 3 x 10-25 kg m2 s-2Therefore, v2 = [2 x (3 x 10-25 kg m2 s-2)] / 9.1 x 10-31 kg=> v2= 65.9 x 104 m2 s-2=>v = 8.12 x 102 m s-1To calculate the wavelength of the electronAccording to de Broglie’s equation, λ=h/mv = (6.626 x 10-34 kg m2 s-1) / (9.1 x 10-31 kg) x (8.12 x 102 m s-1)= 0.08967 x 10-5 m = 8967 x 10-10 m = 8967Å

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Ncert Solutions Chemistry Class 11th Chemistry Class 11th Structure of Atoms

The mass of an electron is 9.1 × 10^-31 kg. If its kinetic energy is 3.0 × 10^-25 J, calculate its wavelength.

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Payal Gupta | Contributor-Level 10

3 months ago

Kinetic energy. K.E. = ½ mv²

=> v²= (2 x K.E.) / m

Given, K.E. = 3 x 10^-25 J = 3 x 10^-25 kg m² s^-2

Therefore, v²= [2 x (3 x 10^-25 kg m² s^-2)] / 9.1 x 10^-31 kg

=> v²= 65.9 x 10⁴ m² s^-2

=>v = 8.12 x 10² m s^-1

To calculate the wavelength of the electron

According to de Broglie’s equation,

λ=h/mv = (6.626 x 10^-34 kg m² s^-1) / (9.1 x 10^-31 kg) x (8.12 x 10² m s^-1)

= 0.08967 x 10^-5 m = 8967 x 10^-10 m = 8967Å

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