Nuclei

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Answer (c)

Explanation- it is a process in which metal decays spontaneously . so during a span of 1 year it will decay almost half of its original value so it will come close to 5000.

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Explanation- a nuclide 1 is said to be mirror isobar of nuclide 2, if Z₁=N₂ and Z₂= N₁

Now ₁₁Na²³, ₁₂Mg²³ for which Z₂=12=N₁ and N₂ =23-12=11=Z₁

(b) As ₁₂Mg²³ contain even number of protons against ₁₁Na²³ which has odd number of protons (11), therefore Mg has greater binding energy than sodium.

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Explanation- Each particle (neutron and proton) present inside the nucleus is called nucleon .

Let $\lambda ={10}^{-15}m$

$\lambda =\frac{h}{p}$

and KE= PE

$E=hc/\lambda$ = $\frac{6.6*{10}^{-34}*3*{10}^8}{{10}^{-15}*1.6*{10}^{-19}}$  eV

K.E= 10⁹eV

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Explanation- R= 12dis/min per gm and R₀= 16dis/min per gm T_1/2= 5760yr

R= $e^{-\lambda t}$ $e^{\lambda t}$

By taking log

$\lambda tloge=log\frac{R_0}{R}$

$\lambda t$ = log₁₀16/12 $*2.303$

$t=\frac{2.303(log4-log3)}{\lambda }$

= 2.303 (0.6020-4.771)5760/0.6931

  = 2391.20yr

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Explanation-because more number of protons means more repulsive force which leads to instability.

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Explanation- during the collision of electron and positron they form gamma radiation and these gamma particle travels in opposite direction to conserve the momentum.

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Explanation- electron cannot emit radiation while exiting because they absorbs energy in eV which is very low as compared to gamma particle . as they contain energy in MeV

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Explanation- at t=0 (dN/dt)_A= (dN/dt)_B

By drawing a perpendicular line across graph (dN/dt)_A> (dN/dt)_B so decay is faster in A than B

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Explanation- dN/dt= $\lambda N$