1
MCQ (Single Correct Answer)

JEE Main 2016 (Online) 9th April Morning Slot

The total number of orbitals associated with the principal quantum number 5 is :
A
5
B
10
C
20
D
25
2
MCQ (Single Correct Answer)

JEE Main 2017 (Offline)

The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg; charge of electron (e) = 1.60210 × 10-19 C; permittivity of vacuum ($${\varepsilon _0}$$) = 8.854185 × 10-12 kg-1 m-3 A2)
A
4.76 $$\mathop {\rm A}\limits^o $$
B
2.12 $$\mathop {\rm A}\limits^o $$
C
0.529 $$\mathop {\rm A}\limits^o $$
D
1.65 $$\mathop {\rm A}\limits^o $$

Explanation

Radius of an atom in nth orbit,

rn = 0.529 $$ \times {{{n^2}} \over Z}$$

Here n = 2

and for hydrogen atom, atomic number (Z) = 1

$$\therefore$$ r2 = 0.529$$ \times {{{2^2}} \over 1}$$ = 2.12 $$\mathop {\rm A}\limits^o $$
3
MCQ (Single Correct Answer)

JEE Main 2017 (Offline)

The group having isoelectronic species is:
A
O2- , F- , Na+, Mg2+
B
O2- , F- , Na, Mg2+
C
O- , F- , Na+, Mg2+
D
O- , F- , Na, Mg+

Explanation

O2- , F- , Na+ and Mg2+, all have 10 electrons each.
4
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

If the shortest wavelength in Lyman series of hydrogen atom is A, then the longestwavelength in Paschen series of He+ is :
A
$${{5A} \over 9}$$
B
$${{9A} \over 5}$$
C
$${{36A} \over 5}$$
D
$${{36A} \over 7}$$

Explanation

Note :

(1)   In Lyman Series, transition happens in n = 1 state
from n = 2, 3, . . . . . $$ \propto $$

(2)   In Balmer Series, transition happens in n = 2 state
from n = 3, 4, . . . . . $$ \propto $$

(3)   In Paschen Series, transition happens in n = 3 state
from n = 4, 5, . . . . . $$ \propto $$

(4)   In Bracktt Series, transition happens in n = 4 state
from n = 5, 6 . . . . . . $$ \propto $$

(5)   In Pfund Series, transition happens in n = 5 state
from n = 6, 7, . . . . $$ \propto $$

We know,

     $${1 \over \lambda }$$ = Rz2 ($${1 \over {n_1^2}}$$ $$-$$ $${1 \over {n_2^2}}$$)

The shortest wavelength of hydrogen atom in Lyman series is from n1 = 1 to n2 = $$ \propto $$

$$\therefore\,\,\,$$ $${1 \over A}$$ = 12 R ($${1 \over {{1^2}}}$$ $$-$$ $${1 \over {{ \propto ^2}}}$$)    [for hydrogen, z = 1]

$$ \Rightarrow $$ $$\,\,\,$$ $${1 \over A}$$ = R

The longest wavelength in pascal series of He+ is from n1 = 3 to n2 = 4

For He+, z = 2.

$${1 \over \lambda }$$ = RZ2 ($${1 \over {n_1^2}}$$ $$-$$ $${1 \over {n_2^2}}$$)

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over \lambda }$$ = $${1 \over A}$$ (2)2 ($${1 \over {{3^2}}}$$ $$-$$ $${1 \over {{4^2}}}$$)

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over \lambda }$$ = $${4 \over A}$$ $$\left( {{7 \over {16 \times 9}}} \right)$$ = $${7 \over {36A}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$\lambda $$ = $${{36A} \over 7}$$

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