Вопрос
Example 15 If the electron accelerated by a potential difference of 10 Vhas de Broglie wavelength of 10^-10m then electron accelerated by a potential difference of 20 VFind a wavelength of (nm)
Решения
4.6
(362 Голоса)
Урий
мастер · Репетитор 5 лет
Ответ
To solve this problem, we can use the de Broglie equation, which relates the wavelength of a particle to its momentum:λ = h / pwhere λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.Given information:- The electron is accelerated by a potential difference of 10 V.- The de Broglie wavelength of the electron is 10^-10 m.We need to find the wavelength of the electron when it is accelerated by a potential difference of 20 V.Step 1: Calculate the momentum of the electron when accelerated by a potential difference of 10 V.Using the de Broglie equation, we can write:λ = h / pp = h / λSubstituting the given values:p = h / (10^-10 m)p = 6.626 × 10^-34 J·s / (10^-10 m)p = 6.626 × 10^-24 kg·m/sStep 2: Calculate the momentum of the electron when accelerated by a potential difference of 20 V.The momentum of the electron is directly proportional to the square root of the potential difference. Therefore, when the potential difference is doubled, the momentum will also be doubled.p' = 2 × pp' = 2 × (6.626 × 10^-24 kg·m/s)p' = 1.325 × 10^-23 kg·m/sStep 3: Calculate the wavelength of the electron when accelerated by a potential difference of 20 V.Using the de Broglie equation again:λ' = h / p'λ' = 6.626 × 10^-34 J·s / (1.325 × 10^-23 kg·m/s)λ' = 5.00 × 10^-11 mTherefore, the wavelength of the electron when accelerated by a potential difference of 20 V is 5.00 × 10^-11 m or 0.05 nm.