An electron of mass m with an initial velocity $\vec{V} = V_{o} \hat{i} (V_{o} > 0)$ enters an electric field $\vec{E} = - E_{o} \hat{i}$ (E₀ constant >0) at t = 0. if λ₀ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is

$\frac{λ_{0}}{(1 + \frac{e E_{0}}{m V_{0}} t)}$

$λ_{o} (1 + \frac{e E_{0}}{m V_{0}} t)$

$λ_{0}$

$λ_{0} t$

Solution

$\frac{λ_{0}}{(1 + \frac{e E_{0}}{m V_{0}} t)}$

Initial de-Brogile wavelength

$λ_{0} = \frac{h}{m V_{0}} . . . . (i)$

Acceleration of electron

$a = \frac{e E_{0}}{m} (∵ F - m a = e E_{0}) V e l o c i t y a f t e r t i m e' t' V = (V_{0} + \frac{e E_{0}}{m} t) S o, λ = \frac{h}{m V} = \frac{h}{m (V_{0} + \frac{e E_{0}}{m} t)} S o, λ = \frac{h}{m V_{0} [1 + \frac{e E_{0}}{m V_{0}} t]} = \frac{λ_{0}}{[1 + \frac{e E_{0}}{m V_{0}} t]} . . . (i i) D i v i d i n g e q s (i i) b y (i) d e - B r o g l i e w a v e l e n g t h λ = \frac{λ_{0}}{1 + \frac{e E_{0}}{m V_{0}} t}$

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Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

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Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

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An electron of mass m with an initial velocity V→ = Voi^ (Vo>0) enters an electric field E→ = - Eo i^ (E0 constant >0) at t = 0. if λ0 is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is λ01+eE0mV0t λo1 + eE0mV0t λ0 λ0t

Some More Questions From Atoms Chapter

Four nuclei of an element undergo fusion to form a heavier nucleus, with the release of energy. Which of the two — the parent or the daughter nucleus — would have higher binding energy per nucleon?

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

The energy spectrum of β-particles [number N(E) as a function of β-energy E] emitted from a radioactive source is

Mock Test Series

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