SATHEE: Modern Physics 7 Question 83

Modern Physics 7 Question 83

13. A nucleus $A$ , with a finite de-Broglie wavelength $λ_{A}$ , undergoes spontaneous fission into two nuclei $B$ and $C$ of equal mass. $B$ flies in the same directions as that of $A$ , while $C$ flies in the opposite direction with a velocity equal to half of that of $B$ . The de-Broglie wavelengths $λ_{B}$ and $λ_{C}$ of $B$ and $C$ respectively

(Main 2019, 8 April II)

(a) $2 λ_{A}, λ_{A}$

(b) $\frac{λ_{A}}{2}, λ_{A}$

(d) $λ_{A}, \frac{λ_{A}}{2}$

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Solution:

Let $m$ be the mass of nuclei $B$ and $C$ .

So, the given situation can be shown in the figure below

Now, according to the conservation of linear momentum, Initial momentum $=$ Final momentum

$\begin{aligned} \Rightarrow p_{A} & = p_{B} + p_{C} or 2 m v_{A} = m v_{B} + m v_{C} \\ 2 m v_{A} & = m v_{B} - \frac{m v_{B}}{2} \\ \Rightarrow 2 v_{A} & = \frac{1}{2} v_{B} \Rightarrow v_{B} = 4 v_{A} \\ and v_{C} & = \frac{v_{B}}{2} = 2 v_{A} \end{aligned}$

So, momentum of $B$ and $C$ respectively, can now be given as

$p_{B} = m_{B} v_{B} = m 4 v_{A} = 2 (2 m v_{A})$

or $p_{B} = 2 p_{A}$

and $p_{C} = m_{C} v_{C} = m 2 v_{A}$ [using Eq. (ii)]

or $p_{C} = p_{A}$

From the relation of de-Broglie wavelength, i.e. $λ = \frac{h}{p}$

where, $p$ is momentum and $h$ is Planck’s constant.

So, for $A, λ_{A} = \frac{h}{p_{A}}$ or $p_{A} = \frac{h}{λ_{A}}$

From Eq. (v), $λ_{B}$ can be written as

$λ_{B} = \frac{h}{2 \times \frac{h}{λ_{A}}} = \frac{λ_{A}}{2}$

Similarly, for $C, λ_{C} = \frac{h}{p_{C}} = \frac{h}{p_{A}}$

[using Eq. (iv)]

Similarly, from Eq. (v), $λ_{C}$ can be written as

$λ_{C} = \frac{h}{\frac{h}{λ_{A}}} = λ_{A}$

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अगला

Modern Physics 7 Question 83

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Modern Physics 7 Question 83

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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