Introduction to Quantum Mechanical Model

Q. The wave function ${\psi }_{n,l,m}$ is a mathematical function whose value depends upon spherical polar coordinates $(r,\theta ,\varphi )$ of the electron and characterized by the quantum numbers n, l and $m_l$. Here r is distance from nucleus, $\theta$ is colatitude and $\varphi$ is azimuth. In the mathematical functions given in the table, Z is atomic number and $a_0$ is Bohr radius.

For the given orbital in Column-I, the only CORRECT combination for any hydrogen-like species is:

1. (IV) (iv) (R)
2. (II) (ii) (P)
3. (III) (iii) (P)
4. (I) (ii) (S)

Q. The wave function ${\psi }_{n,l,m}$ is a mathematical function whose value depends upon spherical polar coordinates $(r,\theta ,\varphi )$ of the electron and characterized by the quantum numbers n, l and $m_l$. Here r is distance from nucleus, $\theta$ is colatitude and $\varphi$ is azimuth. In the mathematical functions given in the table, Z is atomic number and $a_0$ is Bohr radius.

For hydrogen atom, the only CORRECT combination is

1. (I) (iv) (R)
2. (I) (i) (P)
3. (II) (i) (Q)
4. (I) (i) (S)

Q. In an atom, the total number of electrons having the quantum numbers $n=4,|m_l|=1$ and $m_s=-\frac{1}{2}$, is

Q. Calculate the minimum and maximum number of electrons which may have magnetic quantum number, $m=+1$ and spin quantum number, $s=-\frac{1}{2}$ in chromium $\left(Cr\right)$

1. $0,1$
2. $1,2$
3. $4,6$
4. $2,3$