Physics, asked by shantilatabehera87, 9 months ago

An alpha particle of kinetic energy 7.68 Mev is projected towards the nucleus of copper. Calculate it's nearest approach?

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Answers

Answered by BrainlyRonaldo

$\bigstar$ Answer:

$\checkmark$ Given:

An alpha particle of kinetic energy 7.68 MeV

$\checkmark$ To Find:

Distance of Nearest Approach ( $\sf r_0$ )

$\checkmark$ Solution:

We know that,

Distance of Nearest Approach ( $\sf r_0$ )

$\red{\boxed{\sf r_0=\dfrac{1}{4 \pi \epsilon_{0}} \times \dfrac{(2e)(Ze)}{E}}}$

Given that,

$\blue{\sf E = 7.68\; MeV = 7.68 \times 10^6 \times 1.6 \times 10^{-19}\;J}$

$\blue{\sf Z=29}$

Substituting the above values in the formula,

We get,

$\pink{\sf r_{0}=9 \times 10^{9} \times \dfrac{2 \times 29 \times (1.6 \times 10^{-19})^{2}}{7.68 \times 10^{6} \times (1.6 \times 10^{-19})}}$

$\purple{\implies \sf r_0=\dfrac{108.75 \times 10^{9} \times 10^{-38}}{10^{-19+6}}}$

$\red{\implies \sf r_0=\dfrac{108.75 \times 10^{-29}}{10^{-13}}}$

$\red{\implies\sf\:r_{0}=108.75 \times 10^{-29+13}}$

$\blue{\implies \sf r_0 = 108.75 \times 10^{-16}\;metre}$

$\green{\boxed{\boxed{\sf r_0 = 108.75 \times 10^{-16}}}}$

Hence,

Distance of Nearest Approach

$\pink{\large{\bold{\sf r_0 = 108.75 \times 10^{-16}}}}$

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Answered by kailashmeena123rm

$\red{ \sf{Answer}}$

$ \red{ \sf{Formula \: \: used }}$ $ \rightarrow \: E_k = \frac{1}{4\pi\epsilon_\circ} \frac{(2e)(ze)}{r_\circ}$

where

Ek is energy
Z is atomic number
ro is distance of closest approach

$\\$

$\red{ \sf{Solution }}$

$ \rightarrow \: E_k = \frac{1}{4\pi\epsilon_\circ} \frac{(2e)(ze)}{r_\circ}$

here

Ek = 7.68 × $10^6$ ev
1/4πe0 = $9 × 10^9$
Z = 29
e = charge on 1 electron

$\\$

now putting values

$\rightarrow \: 7.68 \times 10^6 \times 1.6 \times {10}^{ - 19} = \frac{9 × 10^9 \times 2 \times 29 \times 1.6 \times {10}^{ - 19} \times 1.6 \times {10}^{ - 19} }{r_\circ} $

$\\$

$\rightarrow \: 7.68 \times 10^6 = \frac{9 × 10^9 \times 2 \times 29 \times 1.6 \times {10}^{ - 19} }{r_\circ} $

$\\$

$\rightarrow r_\circ = 1.09 ×10 ^{-16 }cm$

For more information about distance of closest approach click here

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An alpha particle of kinetic energy 7.68 Mev is projected towards the nucleus of copper. Calculate it's nearest approach?​

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Answer:

Distance of Nearest Approach

An alpha particle of kinetic energy 7.68 Mev is projected towards the nucleus of copper. Calculate it's nearest approach?

$\bigstar$ Answer: