Question

What is the wavelength for the electron accelerated by 10⁴/volts?

Answer 1

Answer:

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Explanation:

Step I. Calculating of the velocity of electron <br> Energy (kinetic energy ) of electron

volts. <br>

<br>

<br> or

<br> or

<br> Step II. calculation of the wavelength of electron <br> According to de Broglie equation, <br>

.

Answer 2

Energy (kinetic energy ) of electron,

E = 1 × 10⁴ eV

⇒ E =1 × 10⁴ × 1.6 × 10⁻¹⁹

⇒ E = 1.6 × 10⁻¹⁵ J

⇒ E = 1.6 × 10⁻¹⁵ kg m² s⁻²

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1/2 mv² = 1.6 × 10⁻¹⁵  

⇒ 1/2 × 9.1 × 10⁻³¹ × v² = 1.6 × 10⁻¹⁵  

⇒ v = 5.93 × 10⁷ ms⁻¹

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According to de Broglie equation,

λ = h/mv

⇒ λ = (6.626 × 10⁻³⁴)/(9.1 × 10⁻³¹)(5.93 × 10⁷)

⇒ λ = 1.22 × 10⁻¹¹ m

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∴ Wavelength (λ) = 1.22 × 10⁻¹¹ m