Q: Consider a helium He atom that absorbs a photon of wavelength 330 nm . The change in the velocity (in cm s - 1 ) of He atom after the photon absorption is ______ . (Assume: Momentum is c

P = h λ mv = h λ v = h mλ v = 6 .6 × 10 − 34 × 6 × 10 23 4 × 10 − 3 × 330 × 10 − 9 v = 3 × 10 − 1 m / s v = 30 cm / s ∆ v = v f - v i = v - 0 = v = 30 cm / s

Q: The figure below is the plot of potential energy versus internuclear distance ( d ) of H 2 molecule in the electronic ground state. What is the value of the net potential energy E 0 (as indicated in t

For one H atom P . E . =- kq 1 q 2 r =- 9 × 10 9 × 1 .6 × 10 − 19 2 0 .529 × 10 − 10 =- 9 × 1 . 6 × 1 . 6 0 . 529 × 10 - 19 Total potential energy for 2 H-atom (per mole) =- 2 × 9 × 1 .6 × 1 .6 0 .529 × 10 − 19 × 6 × 10 23 = -5246 .5 kJ / mole

Question 1

The 2s and the 2p orbital energies of hydrogen atom are E_ 2s ( H ) and E_ 2p ( H ), respectively. The 2s and the 2p orbital energies of lithium atom are E_ 2s ( Li ) and E_ 2p ( Li ), respectively. T

Accepted Answer

For hydrogen atom (a single-electron system), the energy of an orbital depends only on the principal quantum number n. Thus, the 2s and 2p orbitals are degenerate. E_ 2s ( H ) = E_ 2p ( H ) For lithium atom (a multi-electron system), the energy depends on both n and l. Due to the penetration effect, the 2s electron penetrates closer to the nucleus and experiences a higher effective nuclear charge than the 2p electron. Thus, the 2s orbital has lower energy than the 2p orbital. E_ 2s ( Li ) The en

Question 2

X ^ a+ and Y ^ b+ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers n = 1 and n = 2 of X ^ a+ is . The wavelength of l

Accepted Answer

For a hydrogen-like species, the wavelength of the absorbed light during a transition from n_1 to n_2 is given by the Rydberg formula: 1 = R Z^2 ( 1 n_1^2 - 1 n_2^2 ) For X ^ a+ , the transition is from n = 1 to n = 2: 1 = R Z_X^2 ( 1 1^2 - 1 2^2 ) = 3 4 R Z_X^2 = 4 3 R Z_X^2 For Y ^ b+ , the transition is from n = 2 to n = 4: 1 9 = R Z_Y^2 ( 1 2^2 - 1 4^2 ) = R Z_Y^2 ( 1 4 - 1 16 ) = 3 16 R Z_Y^2 9 = 16 3 R Z_Y^2 Substituting the expression for from the first equation into the second: 9 ( 4 3 R

Question 3

According to Bohr's model, the highest kinetic energy is associated with the electron in the

Accepted Answer

K E=+13.6 Z^2 n^2 (A) KE _ 1,11 =+13.6 1^2 1^2 =13.6 eV (B) KE _ 1, Hc =+13.6 2^2 1^2 =13.6 4 eV (C) KE _ 2, He ^ + =+13.6 2^2 2^2 =13.6 eV (D) KE _ 2, Li ^ i ^ + =+13.6 3^2 2^2 =13.6 9 4 eV

Question 4

Among the following, the correct statement(s) for electrons in an atom is(are)

Accepted Answer

(1) Uncertainity principle talks about probability of finding electrons in different regions around the nucleus rather than definite paths. (2) With increase in distance of electron from the nucleus, its energy increases. (3) Energy of electron E_n=-13.6 Z ^2 n ^2 eV / atom. (4) Velocity of electron V_n=2.19 10^6 Z n ~m / sec .

Question 5

For He + , a transition takes place from the orbit of radius 105 . 8 pm to the orbit of radius 26 . 45 pm . The wavelength (in nm ) of the emitted photon during the transition is Bohr radius, a = 52 .

Accepted Answer

The radius of the n th  orbit can be represented as, r = 52 . 9 &#215; n 2 z pm &#8756; &#160;&#160; 105 . 8 = 52 . 9 &#215; n 2 2 &#160;&#160; &#8756; n 2 = 2 and  26 . 45 = 52 . 9 &#215; n 2 2 &#160;&#160; &#8756; n 1 = 1 &#8757; &#916;E = R H hC &#215; z 2 1 n 1 2 - 1 n 2 2 hc &#955; = R H hC &#215; z 2 1 n 1 2 - 1 n 2 2 6 . 6 &#215; 10 - 34 &#215; 3 &#215; 10 8 &#955; = 2 . 2 &#215; 10 - 18 &#215; 4 &#215; 1 1 - 1 4 6 . 6 &#215; 10 - 34 &#215; 3 &#215; 10 8 &#955; = 2 . 2 &#215; 10

Question 6

Consider a helium He atom that absorbs a photon of wavelength 330 &#160; nm . The change in the velocity (in cm &#160; s - 1 ) of He atom after the photon absorption is ______ . (Assume: Momentum is c

Accepted Answer

P = h &#955; mv = h &#955; v = h m&#955; v = 6 .6 &#215; 10 &#8722; 34 &#215; 6 &#215; 10 23 4 &#215; 10 &#8722; 3 &#215; 330 &#215; 10 &#8722; 9 v = 3 &#215; 10 &#8722; 1 &#160; m / s v = 30 &#160; cm / s &#8710; v &#160; = &#160; v f - v i = v - 0 = v &#160; = &#160; 30 &#160; cm / s

Question 7

The figure below is the plot of potential energy versus internuclear distance ( d ) of H 2 molecule in the electronic ground state. What is the value of the net potential energy E 0 (as indicated in t

Accepted Answer

For one H atom P . E . &#8196; =- kq 1 q 2 r =- 9 &#215; 10 9 &#215; 1 .6 &#215; 10 &#8722; 19 2 0 .529 &#215; 10 &#8722; 10 =- 9 &#215; 1 . 6 &#215; 1 . 6 0 . 529 &#215; 10 - 19 Total potential energy for 2 H-atom (per mole) =- 2 &#215; 9 &#215; 1 .6 &#215; 1 .6 0 .529 &#215; 10 &#8722; 19 &#215; 6 &#215; 10 23 = -5246 .5 &#8196; kJ / mole

Question 8

The ground state energy of hydrogen atom is - 13.6 &#160; e V . Consider an electronic state &#936; of H e + whose energy, azimuthal quantum number and magnetic quantum number are - 3.4 &#160; e V , &

Accepted Answer

∵ E H e + = - 13.6 z 2 n 2 = - 13.6 2 2 n 2 = - 3.4 n 2 = 16 ∴ n = 4 n = 4 , l = 2 , m = 0 belongs to 4 d y z orbital → Radial nodes ⇒ n - l - 1 → Angular nodes ⇒ 4 - 2 - 1 = 1 → Angular nodes ⇒ l ⇒ 2 Since H e + is a single e - ion, its nuclear charge experienced.

Question 9

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the n t h orbit of the atom and List-II contains

Accepted Answer

According to Bohr’s atomic model: Radius of orbit ∝ n 2 Angular Momentum ∝ n Kinetic energy ∝ 1 n 2 Potential energy ∝ - 1 n 2

Question 10

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the n t h orbit of the atom and List-II contains

Accepted Answer

According to Bohr’s atomic model: Radius of orbit ∝ n 2 Angular Momentum ∝ n Kinetic energy ∝ 1 n 2 Potential energy ∝ - 1 n 2

Structure of Atom — Previous Year Questions & Solutions