List of top Physical Chemistry Questions on Atomic Structure asked in Indian Institute Of Technology Joint Admission Test for MSc

An element E has three isotopes:
\(28\\14 E\) (abundance 92.21%, atomic mass: 27.977 a.m.u.), 
\(29\\14 E\) (abundance 4.70%, atomic mass: 28.976 a.m.u.), and 
\(30\\14 E\) (abundance 3.09%, atomic mass: 29.974 a.m.u). 
The atomic mass of E is _______ a.m.u. 
(rounded off to three decimal places

Consider the wavefunction 𝜓(𝑥) = 𝑁[exp(𝑖𝑘𝑥) + exp(−𝑖𝑘𝑥)]. The complex conjugate 𝜓 ∗ (𝑥) is [Given: 𝑁 is the normalization constant; 𝑖=\(\sqrt-1\)]

Consider photoelectric effect. The number of incident photons is the same for all frequencies. The plot that best describes the dependence of the number of photoelectrons (n) emitted as a function of the incident light frequency (ν) is

The magnitude of energy difference between the energy levels 𝑛=3 and 𝑛=2 of a quantum particle of mass 𝑚 in a box of length L is \(\frac{Xℎ ^2}{ 8𝑚L ^2} .\) 
Then X = _______. 
(rounded off to the nearest integer) 
[Given: ℎ is Planck’s constant and 𝑛 denotes the quantum number]

The system with the lowest zero-point energy when it is confined to a one dimensional box of length 𝐿 is

The following diagram shows the kinetic energy of the ejected photoelectrons against the energy of incident radiation for two metal surfaces M₁ and M₂. If the energy of the incident radiation on M₁ is equal to the work function of M₂, the de Broglie wavelength of the ejected photoelectron is nm

[Given: Mass of electron = 9.11x10⁻³¹ kg; Planck’s constant = 6.62x10⁻³⁴ J s; 1 eV=1.6x10⁻¹⁹ J.]
(round off to two decimal places)

The ratio of the $2p → 1s$ transition energy in $He^+$ to that in the H atom is closest to

The potential for a particle in a one-dimensional box is given as:
$V(x)=0$ for $0≤x≤L,$ and $V(x) = ∞$ elsewhere.
The locations of the internal nodes of the eigenfunctions $\Psi _n(x), n≥2$, are
[Given: m is an integer such that 0<m<n]