Assertion $(A)$: The probability of finding an electron in a small volume around a point $(x, y, z)$ at a distance $r$ from the nucleus is proportional to $\psi^2$.
Reason $(R)$: Subatomic particles possess both particle and wave nature.

What is the nature of the solution to the $Schrodinger$ wave equation for multi-electron atoms? How is it handled?

Given below are two statements $:$
Statement $(I):$ It is impossible to specify simultaneously with arbitrary precision,both the linear momentum and the position of a particle.
Statement $(II) :$ If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron,then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{h}{4\pi}} \times \frac{1}{m}$ which simplifies to $\geq \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. In the light of the above statements,choose the correct answer from the options given below $:$

An electron is moving with a velocity of $600 \, m/s$ with an accuracy of $0.005\%$. The uncertainty in its position will be: ($h = 6.6 \times 10^{-34} \, kg \, m^2 \, s^{-1}$,mass of electron $m_e = 9.1 \times 10^{-31} \, kg$)

If the position of the electron is measured within an accuracy of $\pm 0.002 \,nm$,calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is $\frac{h}{4 \pi \times 0.05 \,nm}$,is there any problem in defining this value?

If the uncertainty in position and momentum of a particle are equal,then what will be the uncertainty in the momentum of the particle?