Class 12th

This is a Short Answer Type Questions as classified in NCERT Exemplar

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

This is a Short Answer Type Questions as classified in NCERT Exemplar

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

This is a Short Answer Type Questions as classified in NCERT Exemplar

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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This is a Short Answer Type Questions as classified in NCERT Exemplar

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

This is a Short Answer Type Questions as classified in NCERT Exemplar

Explanation- dN/dt= $\lambda N$

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This is a Short Answer Type Questions as classified in NCERT Exemplar

Explanation- nuclei ₂He⁴ and ₁He³ have the same mass number . the element having more number of proton having more repusion so less binding energy. So ₂He⁴ have more number of proton so more repulsion so less binding energy.

$\begin{array}{l}{\displaystyle {\int }_0^2\frac{6x+3}{x^2+4}}dx={\displaystyle {\int }_0^2\frac{6x}{x^2+4}}dx+{\displaystyle {\int }_0^2\frac{3}{x^2+4}}dx\\ =3{\displaystyle {\int }_0^2\frac{2x}{x^2+4}}dx+3{\displaystyle {\int }_0^2\frac{1}{x^2+2^2}}dx\\ =3{\left[log\left|x^2+4\right|\right]}_0^2+\frac{3}{2}{\left[ta{n}^{-1}\frac{x}{2}\right]}_0^2\\ =3\left[log\left|2^2+4\right|-log\left|0^2+4\right|\right]+\frac{3}{2}\left[ta{n}^{-1}\frac{2}{2}-ta{n}^{-1}\frac{0}{2}\right]\\ =3\left[log\frac{8}{4}\right]+\frac{3}{2}[\pi /4-0]\\ =3log2+\frac{\mathrm{3\pi }}{}\end{array}$