Physics MCQs for NEET — Practice Questions with Answers

The activity of a radioactive substance is

$$\begin{gathered} R=R_0{\left(\frac{1}{2}\right)}^n \\ [R=Final number] \\ [R_0=Initial number] \end{gathered}$$

Here, n = number of half-lives

$$\begin{gathered} =\frac{t}{T_{1/2}}=\frac{24}{6}=4 [T_{1/2}=Half life period] \\ and R=0.01 \mu Ci \\ So, 0.01 =R_0{\left(\frac{1}{2}\right)}^4 \\ or R_0=0.01\times {\left(2\right)}^4=0.01\times 16 \\ =0.16 \mu Ci \end{gathered}$$

$R=R_0{A}^{1/3}\Rightarrow R \alpha A^{1/3}$

Fraction undecayed is ${\left(\frac{1}{2}\right)}^5=\frac{1}{32}$

When a nucleus is formed, then the mass of nucleus is slightly less than the sum of masses of Z protons and N neutrons.

i.e., $m<\left(Z{m}_p+N{m}_n\right)$

Isotones are the nuclides which contain the same number of neutrons. In ${}_{6}C_{13} and {}_{7}N_{14}$, number of neutrons in carbon = 13 - 6 = 7 and number of neutrons in nitrogen = 14 - 7 = 7.

Note:-

No. of neutrons is given by

mass no.(A) - atomic no. (Z)

$\frac{3}{4}th$ active decay takes place in time

$t=2\left(T_{1/2}\right)\Rightarrow \frac{3}{4}=2\left(T_{1/2}\right)\Rightarrow T_{1/2}=\frac{3}{8} s$

Electronic configuration of iodine (53) is = 2, 8, 18, 18, 7

$\therefore$ Principal quantum number n = 5

Radius of nth orbit is given by 

$$\begin{gathered} r_n=r_0\left(\frac{n^2}{Z}\right) (Z=atomic number) \\ where r_0=0.53 \stackrel{0}{A}=0.53\times {10}^{-10} m \\ \therefore r_n=(0.53\times {10}^{-10})\times \frac{5^2}{53} \\ =2.5\times {10}^{-11} m \end{gathered}$$

Nuclear forces are the short range forces of attraction which hold together the nucleons (neutrons and protons) in the tiny nucleus of an atom, inspite of strong electrostatic forces of repulsion between protons. Nuclear forces are charge independent forces. They are the strongest forces in nature. The magnitude of nuclear forces is 100 times that of electrostatic forces and ${10}^{38}$ times that of gravitational forces between nucleons. They are operative upto distances of the order of a few fermi. They are non-central forces.

Experimental measurements show that volume of a nucleus is proportional to its mass number A. If R is the radius of the nucleus assumed to be spherical, then its volume and mass no. relation is given by

Volume (V) $\alpha$ mass no. (A)

$$\begin{gathered} or \left(\frac{4}{3}{\mathrm{\pi R}}^3\right) \alpha A \\ or R \alpha A^{1/3} \\ \therefore \frac{R_{Al}}{R_{Te}}=\frac{{\left(27\right)}^{1/3}}{{\left(125\right)}^{1/3}}=\frac{3}{5}=\frac{6}{10} \end{gathered}$$

Bragg's law for different of X-rays is

$2d \sin \theta =n\lambda$