Explanation Write the expression to obtain the wavelength. λ = h m v Here, λ is the wavelength, h is the Planck’s constant, m is the mass and v is the velocity. Re-arrange the above equation. v = h m λ (I) The potential difference of an electron is equal to its kinetic energy. Write the expression to obtain the potential difference must an electron be accelerated. P = 1 2 m v 2 (II) Here, P is the potential difference of an electron, m is the mass of an electron and v is the velocity. Conclusion: Substitute 6.63 × 10 − 34 J ⋅ s for h , 9.1 × 10 − 31 kg for m and 0.21 nm for λ in equation (I) to calculate v . v = 6.63 × 10 − 34 J ⋅ s ( 9.1 × 10 − 31 kg ) ( 0.21 nm ) = 6.63 × 10 − 34 J ⋅ s ( 9.1 × 10 − 31 kg ) ( 0.21 nm × 1 m 10 9 nm ) = 6.63 × 10 − 34 J ⋅ s ( 9.1 × 10 − 31 kg ) ( 0.21 × 10 − 9 m ) = 6.63 × 10 − 34 J ⋅ s 1

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Chapter 37, Problem 42P

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The value of a potential difference through which an electron must be accelerated to achieve a wavelength of 0.21 nm.

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Chapter 37, Problem 41P

Chapter 37, Problem 43P

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