The energy absorbed by each molecule (A₂) of a substance is 4.4 × 10^-19 J and bond energy per molecule is 4.0 × 10^-19J. The kinetic energy of the molecule per atom will be:

2.2 × 10^-19 J
2.0 × 10^-19 J
4.0 × 10^-20 J
2.0 × 10^-20 J

Solution

If uncertainty in position and momentum are equal, then uncertainty in velocity is :

\(\frac{1}{2m}\sqrt{\frac{h}{\pi}}\)
\(\sqrt{\frac{h}{2 \pi}}\)
\(\frac{1}{m}\sqrt{\frac{h}{\pi}}\)
\(\sqrt{\frac{h}{\pi}}\)

Solution

The magnetic moments of Cu(Z = 29), Ti (Z = 22), and Cr (Z = 24) are in the ratio of

1 : √5 : 4
4 : √5 : 1
1 : 2 : 6
1 : √3 : √21

The magnetic moment of M^x+ (atomic number of M = 25) is √15 B.M. The number of unpaired electrons and the value of x respectively are

4, 3
3, 4
3, 2
5, 2

Solution

\(\sqrt{n\left ( n + 2 \right )} = \sqrt{15}\), n = 3 (n = number of unpaired electrons)

Therfore, x = 4

∵ M⁴⁺ = [Ar]3d³

The five d-orbitals are designated as d_xy, d_yz, d_xz, d_{x² – y²} and d_z². Choose the correct statement.

The shapes of the first three orbitals are similar but that of the fourth and fifth orbitals are different
The shapes of all five d-orbitals are similar
The shapes of the first four orbitals are similar but that of the fifth orbital is different
Ths shapes of all five d-orbitals are different

Solution

First four orbitals contain four lobes, while fifth orbital consists of only two lobes. The lobes of d_xy orbital lie between x and y axis. Similarly in the case of d_yz and d_zx. their lobes lie between yz and zx axis respectively. Four lobes of d_{x² - y²} orbital are lying along x and y axis while two lobes of d_z² orbital are lying along z-axis.

If the de-Broglie wavelength of a particle of mass m is 100 times its velocity, then its value in terms of its mass (m) and Planck’s constant (h) is

\(\frac{1}{10}\sqrt{\frac{m}{h}}\)
\(10\sqrt{\frac{h}{m}}\)
\(\frac{1}{10}\sqrt{\frac{h}{m}}\)
\(10\sqrt{\frac{m}{h}}\)

Solution

The magnetic moment of a particular ion is 2√6 B.M. The ion is

Mn²⁺
Fe³⁺
Co²⁺
Co³⁺

Solution

Magnetic moment

= \(2\sqrt{6} = \sqrt{24} \; B.M. \; = \; \sqrt{n \left(n + 2 \right)} \; B.M.\)

Hence, n = 4 (unpaired electrons)

Co³⁺ – [Ar] 3d⁶, 4 unpaired electrons.

Which one of the following is not the characteristic of Planck’s quantum theory of radiation?

The energy is not absorbed or emitted in whole number or multiple of quantum
Radiation is associated with energy
Radiation energy is not emitted or absorbed continuously but in the form of small packets called quanta
This magnitude of energy associated with a quantum is proportional to the frequency.

Solution

Energy is always absorbed or emitted in whole number or multiples of quantum.

Number of protons, neutrons and electrons in the element \(_{89}^{231}\textrm{Y}\) is

89, 231, 89
89, 89, 242
89, 142, 89
89, 71, 89

Solution

In \(_{89}^{231}\textrm{Y}\) number of protons and electrons is 89 and number of neutrons = A – Z = 231 – 89 = 142

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