Question

if an electron beam in a t.v. picture tube is accelerated by 10,000V calculate the debroglie wavelength of an electron


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Answer 1

Hi,This is your Answer Happy Learning.

Answer 2

Given info : An electron beam in a TV picture tube is accelerated by 10,000 volts.

To find : The De-Broglie's wavelength of an electron is ...

solution : energy of an electron = voltage × charge on each electron

⇒E = 10000 V × 1.6 × 10^-19 C

= 1.6 × 10¯¹⁵ J

now energy = P²/2m

⇒E = P²/2m

⇒P = √(2mE)

Therefore the De-Broglie's wavelength, λ = h/√(2mE)

⇒λ = (6.63 × 10¯³⁴ Js )/√(2 × 9.1 × 10¯³¹ kg × 1.6 × 10¯¹⁵ J)

= (6.63 × 10¯³⁴)/√(18.2 × 1.6 × 10¯⁴⁶)

= 1.2286 × 10¯¹¹ m

= 12.286 pm ≈ 12.23 pm

Therefore the wavelength of an electron would be 12.23 pm