Quantum Mechanical Model of Atom

(a) How many subshells are associated with$\mathrm{n}=4$ ? (b) How many electrons will be present in the subshells having ${\mathrm{m}}_{\mathrm{s}}$ value of $-1/2$ for $\mathrm{n}=4$ ?

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

Explain, giving reasons, the following set of quantum numbers are possible.
$\mathrm{n}=3, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$

Explain, giving reasons, the following set of quantum numbers are not possible.
$\mathrm{n}=3, \mathrm{l}=3, {\mathrm{m}}_{\mathrm{l}}=–3, {\mathrm{m}}_{\mathrm{s}}=+1/2$

Explain, giving reasons, the following sets of quantum numbers are not possible.
$\mathrm{n}=1, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$

The following set of quantum numbers are possible? Explain.
$\mathrm{n} = 1, \mathrm{l} = 0, {\mathrm{m}}_{\mathrm{l}} = 0, {\mathrm{m}}_{\mathrm{s}} = –½$

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists:

1. $\mathrm{n}=4, \mathrm{l}=2, {\mathrm{m}}_{\mathrm{l}}=–2, {\mathrm{m}}_{\mathrm{s}}=–1/2$
2. $\mathrm{n}=3, \mathrm{l}=2, {\mathrm{m}}_{\mathrm{l}}=1, {\mathrm{m}}_{\mathrm{s}}=+1/2$
3. $\mathrm{n}=4, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$
4. $\mathrm{n}=3, \mathrm{l}=2, {\mathrm{m}}_{\mathrm{l}}=–2, {\mathrm{m}}_{\mathrm{s}}=–1/2$
5. $\mathrm{n}=3, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=–1, {\mathrm{m}}_{\mathrm{s}}=+1/2$
6. $\mathrm{n}=4, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+1/2$

If the position of the electron is measured within an accuracy of $\underset{-}{+}0.002 \mathrm{nm}$, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is $\mathrm{h}/4{\mathrm{\pi }}_{\mathrm{m}}\times 0.05\mathrm{nm}$, is there any problem in defining this value.

The velocity associated with a proton moving in a potential difference of $1000 \mathrm{V}$ is $4.37\times {10}^5 {\mathrm{ms}}^{–1}$. If the hockey ball of mass $0.1\mathrm{kg}$ is moving with this velocity, calculate the wavelength associated with this velocity.

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is $800 \mathrm{pm}$, Calculate the characteristic velocity associated with the neutron.

Dual behavior of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is $1.6\times {10}^6 {\mathrm{ms}}^{-1},$ calculate de Broglie wavelength associated with this electron.

How many electrons in an atom may have the following quantum numbers?

(a) $\mathrm{n}=4, {\mathrm{m}}_{\mathrm{s}}=-\frac{1}{2}$
(b) $\mathrm{n}=3, \mathrm{l}=0$

Explain, giving reasons, following set of quantum numbers are possible.
$\mathrm{n}=2, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=-\frac{1}{2}$
 

Given set of quantum numbers are possible or not. Explain?
$\mathrm{n}=0, \mathrm{l}=0, {\mathrm{m}}_{\mathrm{l}}=0, {\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}$