Q: Energy and radius of first Bohr orbit of He ^ + and Li ^ 2+ are [Given R _ H =2.18 10^ -18 ~J , a _0=52.9 pm ]

aligned & E_n=-2.18 10^ -18 Z^2 n^2 J \\ & For He ^ + E _1=-2.18 10^ -18 2^2 1^2 ~J \\ & =-8.72 10^ -18 ~J \\ & For Li ^ 2+ E _1=-2.18 10^ -18 3^2 1^2 ~J \\ & =-19.62 10^ -18 ~J \\ & r _ n =52.9 n ^2 Z pm \\ & For He ^ + r _1=52.9 1^2 2 pm =26.4 pm \\ & For Li ^ 2+ r _1=52.9 1^2 3 pm =17.6 pm aligned

Question 1

A bulb is rated at 150 watt, converting 8\% energy into light. If energy of one photon is 4.42 10^ -19 J, how many photons are emitted by the bulb per second ?

Accepted Answer

Power of the bulb, P = 150 W Energy converted into light per second, E = 8\% of 150 J E = 8 100 150 = 12 J Energy of one photon, E_p = 4.42 10^ -19 J Number of photons emitted per second, n = E E_p n = 12 4.42 10^ -19 n = 2.71 10^ 19 Answer: 2.71 10^ 19

Question 2

Consider the following schematic plots of orbital wavefunction ( _r) against distance (r) from the nucleus. The figure representing two radial nodes in the orbital is

Accepted Answer

A radial node is a point where the radial wavefunction _r becomes zero and changes sign, excluding the origin (r=0) and infinity (r ). In a plot of _r versus r, the number of radial nodes corresponds to the number of times the curve crosses the horizontal axis ( _r = 0). Analyzing the given plots: Figure A: The curve does not cross the r-axis. Number of radial nodes = 0. Figure B: The curve crosses the r-axis once. Number of radial nodes = 1. Figure C: The curve crosses the r-axis twice. Number

Question 3

Match List I with List II : List I (Quantum Numbers) List II (Orbital) 'n' 'l' A. 2 1 I. 3d B. 4 0 II. 2p C. 5 3 III. 4s D. 3 2 IV. 5f Choose the correct answer from the options given below :

Accepted Answer

The principal quantum number n represents the shell, and the azimuthal quantum number l represents the subshell. For l = 0, the subshell is s. For l = 1, the subshell is p. For l = 2, the subshell is d. For l = 3, the subshell is f. A. n = 2, l = 1 corresponds to the 2p orbital. (A II) B. n = 4, l = 0 corresponds to the 4s orbital. (B III) C. n = 5, l = 3 corresponds to the 5f orbital. (C IV) D. n = 3, l = 2 corresponds to the 3d orbital. (D I) The correct matching is A-II, B-III, C-IV, D-I. Ans

Question 4

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n =2 n =3 and n =4 n =6 transitions, respectively, is

Accepted Answer

1 = RZ ^2 ( 1 n _1^2 - 1 n _2^2 ) For 2 3 1 _1 = R (1)^2 ( 1 2^2 - 1 3^2 ) (1) For 4 6 1 _2 = R (1)^2 ( 1 4^2 - 1 6^2 ) (2) Divide (1) & (2) aligned & _2 _1 = 1 2^2 - 1 3^2 1 4^2 - 1 6^2 \ & _2 _1 = 4 1 \ & _1 _2 = 1 4 aligned

Question 5

Energy and radius of first Bohr orbit of He ^ + and Li ^ 2+ are [Given R _ H =2.18 10^ -18 ~J , a _0=52.9 pm ]

Accepted Answer

aligned & E_n=-2.18 10^ -18 Z^2 n^2 J \ & For He ^ + E _1=-2.18 10^ -18 2^2 1^2 ~J \ & =-8.72 10^ -18 ~J \ & For Li ^ 2+ E _1=-2.18 10^ -18 3^2 1^2 ~J \ & =-19.62 10^ -18 ~J \ & r _ n =52.9 n ^2 Z pm \ & For He ^ + r _1=52.9 1^2 2 pm =26.4 pm \ & For Li ^ 2+ r _1=52.9 1^2 3 pm =17.6 pm aligned

Question 6

Given below are two statements: Statement I: The Balmer spectral line for H atom with lowest energy is locateld at 5 36 R_H ~cm ^ -1 . ( R _ H = . Rydberg constant ) Statement II: When the temperature

Accepted Answer

For Balmer series n _1=2 n _2=3 v = 1 =R_H [ 1 n_1^2 - 1 n_2^2 ] v =R_H [ 1 4 - 1 9 ] v = 5 R_H 36 ~cm ^ -1

Question 7

The quantum numbers of four electrons are given below : I. n=4 ; I=2 ; m_1=-2 ; s=- 1 2 II. n=3 ; I=2 ; m_1=1 ; s=+ 1 2 III. n=4 ; I=1 ; m_1=0 ; s=+ 1 2 IV. n=3 ; I=1 ; m_1=-1 ; s=+ 1 2 The correct de

Accepted Answer

(I) n=4, I=2, m_I=-2, s=- 1 2 ; represents 4 d(n+I=6) (II) n=3, I=2, m_l=1, s=+ 1 2 ; represents 3 d(n+I=5) (III) n=4, I=1, m_I=0, s=+ 1 2 ; represents 4 p(n+I=5) (IV) n=3, I=1, m_l=-1, s=+ 1 2 ; represents 3 p(n+I=4) Order of energy depends on the (n+I), greater is the (n+I) value greater is the energy, if (n+I) is same, then it depends on n; if ' n ' is more, energy is more. Step-1: According to ( n + I ) Energy =( I ) ( II )=( III ) ( IV ) Step-2 : If n , then energy increases Energy =( I ) (

Question 8

The energy of an electron in the ground state (n=1) for He ^ + ion is -x J, then that for an electron in n=2 state for Be ^ 3+ ion in J is

Accepted Answer

E_n=-R_H ( z^2 n^2 ) J For He ^ + (n=1), aligned & E_n=-x=-R_H ( 2^2 1^2 )=-4 R_H \ & R_H= x 4 \ & aligned For Be ^ 3+ (n=2), aligned E_n & =-R_H ( z^2 n^2 ) J \ & =- x 4 ( 4 4 2 2 )=-x J aligned

Question 9

Match List I with List II Choose the correct answer from the options given below :

Accepted Answer

- Magnetic quantum number mı informs about orientation of orbital. - Spin quantum number m _ s informs about orientation of spin of electron. - Azimuthal quantum number (I) informs about shape of orbital - Principal quantum number ( n ) informs about size of orbital

Structure of Atom — Previous Year Questions & Solutions