Test: Single Correct MCQs: Structure of Atom | JEE Advanced

No. of neutrons = Mass number – Atomic number                  
= 70 – 30 = 40.

Rutherford’s scattering experiment led to the discovery of nucleus.

One p-orbital can accommodate up to two electrons with opposite spin while p-subshell can accommodate upto six electrons.

The principal quantum number (n) is related to the size of the orbital (n = 1, 2, 3.....)

According to Rutherford's experiment. "The central part consisting of whole of the positive charge and most of the mass, called nucleus, is extremely small in size compared to the size of the atom."

  for neutron    = 0;  α-particle =    = 0.5;

proton = = 1; electron =  = 1837

Rb has the configuration : 1s² 2s²p⁶ 3s²p⁶d¹⁰ 4s²p⁶ 5s¹; so n = 5, l = 0, m = 0 and s = +½ is correct set of quantum numbers for valence shell electron of Rb.

NOTE : Energy is emitted when electron falls from higher energy level to lower energy level and energy is absorbed when electron moves from lower level to higher level. 1s is the lowest energy level of electron in an atom.
∴ An electron in 1s level of hydrogen can absorb energy but cannot emit energy.

Bohr model can explain spectrum of atoms/ions containing one electron only.

The radius of nucleus is of the order of 1.5 × 10^–13 to 6.5 × 10^–13 cm or 1.5 to 6.5 Fermi (1 Fermi = 10^–13 cm)

TIPS/Formulae : The following is the increasing order of wavelength or decreasing order of energy of electromagnetic radiations :

Among given choices radiowaves have maximum wavelength.

Electrons in an atom occupy the extra nuclear region.

If l = 2, m ≠ –3, m will vary from –2 to +2. i.e. possible values of m are –2, –1, 0, + 1 and + 2.

Isotones have same number of neutrons. All atoms in triad (a) have same number of neutrons (= A – Z = 8).

Difference in the energy of the energy levels involved in the transition.

According to Aufbau principle, the orbital of lower energy (2s) should be fully filled before the filling of orbital of higher energy starts.

TIPS/Formulae : The element having highest tendency to accept the electron will be most electronegative element.
Configuration ns², np⁵ means it requires only one electron to attain nearest noble gas configuration. So, it will be most electronegative element among given choices.

NOTE : Exactly half filled orbitals are more stable than nearly half filled orbitals.
Cr (At. no. 24) has configuration [Ar] 3d⁵, 4s¹.

Electronic configuration of chlorine is [Ne] 3s², 3p⁵
∴ Unpaired electron is found in 3p sub-shell.
∴ n = 3, l = 1, m = 1

X-rays can ionise gases and cannot get deflected by electric and magnetic fields, wavelength of these rays is 150 to 0.1Å. Thus the wavelength of X-rays is shorter than that of u.v. rays.

As packet of energy equal to hv; as wave having frequency v.

TIPS/Formulae : Total nodes = n – l
No. of radial nodes = n – l – 1
No. of angular nodes = l
For 3p sub-shell, n = 3, l = 1
∴ No. of radial nodes = n – l – 1 = 3 – 1 – 1 = 1
∴ No. of angular nodes = l = 1

TIPS/Formulae : Orbital angular momentum (mvr) = 

For 2s orbital, l (azimuthal quantum number) = 0

∴ Orbital angular momentum = 0.

The expression for orbital angular momentum is Angular momentum =

For d orbital, l = 2.
Hence, 

TIPS/Formulae : The two guiding rules to arrange the various orbitals in the increasing energy are:
(i) Energy of an orbital increases with increase in the value of n + l.
(ii) Of orbitals having the same value of n + l, the orbital with lower value of n has lower energy.
Thus for the given orbitals, we have
(i)   n + l = 4 + 1 = 5
(ii)  n + l = 4 + 0 = 4
(iii) n + l = 3 + 2 = 5
(iv) n + l = 3 + 1 = 4
Hence, the order of increasing energy is (iv) < (ii) < (iii) < (i)

p_x orbital being dumbell shaped, have number of nodal planes = 1, in yz plane.

3d 54s¹ system is more stable than 3d⁴4s², hence former is the ground state configuration.

TIPS/Formulae : According to de-Broglie’s equation

Given, h = 6.6 × 10^–34 Js, m = 200 × 10^–3 kg

= 2.38 × 10^–30 m

The term spin implies that this magnetic moment is produced by the electron charge as the electron rotates about its own axis. Although this conveys a vivid mental picture of the source of the magnetism, the electron is not an extended body and its rotation is meaningless. Electron spin has no classical counterpart; the magnetic moment is a consequence of relativistic shifts in local space and time due to the high effective velocity of the electron in the atom.

Rutherfor d's experiment was actually α -par ticle scattering experiment. α -Particle is doubly positively charged heliumion i.e., He - nucleus.

As per Pauli Exclusion Principle  "no two electrons in the same atom can have all the four quantum numbers equal or an orbital cannot contain more than two electrons and it can accommodate two electrons only when their directions of spins are opposite".

TIPS/Formulae :​

For hydrogen, n = 1 and Z = 1 ; ∴ r_H = 0.529

For Be³⁺, n = 2 and Z = 4 

TIPS/Formulae : Number of radial nodes = (n - l - 1)
For 3s: n = 3, l = 0 (Number of radial node = 2)
For 2p: n =2, l = 1 (Number of radial node = 0)

Average atomic mass of Fe

As per Bohr’s postulate,

Since, 

So, for 2^nd Bohr orbit

Radial probability function curve for 1s is (D).
Here P is 4πr²R².