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The ionization energy of a hydrogen like Bohr atoms is 4 Rydbergs. (i) What is the wavelength of the radiation emitted when the electrons jumps from the first excited state to the ground state ? (ii) What is the radius of the first orbit for this atom ?

The ionization energy of a hydrogen like Bohr atoms is 4 Rydbergs. (i) What is the wavelength of the radiation emitted when the electrons jumps from the first excited state to the ground state ? (ii) What is the radius of the first orbit for this atom ?

Grade:11

5 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
(i) En = - I.E. / n2 for Bohr’s hydrogen atom.
Here, I.E. = 4R ∴ En = -4R / n2
∴ E2 – E1 = -4R / 22 – (- 4R / l2) = 3 R …(i)
E2 - E1 = hv = hc /λ ….(iii)
From (i) and (ii)
hc / λ = 3R
∴ λ = hc / 3R = 6.6 x 10-34 x 3 x 108 / 2.2 x 10-18 x 3 = 300Å
(ii) The radius of the first orbit
Bohr’s radius of hydrogen atom = 5 x 10-11 m (given)
|En| = + 0.22 x 10-17 Z2 = 4 R = 4 x 2.2 x 10-18
∴ Z = 2
∴ rn­ = r0 / Z = 5 x 10-11 / Z = 5 x 10-11 / 2 = 2.5 x 10-11 m
Jane
12 Points
7 years ago
Ionization energy = 4R = 4*2.2*10^-184* 2.2 * 10^-18 = 13.6 * 1.6 * 10^-19 * z^2=> z = 2 R= Radius of hydrogen / 2R= 5*10^-11/2 = 2.5*10^-11
Jane
12 Points
7 years ago
Ionization energy = 4R = 4*2.2*10^-184* 2.2 * 10^-18 = 13.6 * 1.6 * 10^-19 * z^2=> z = 2R= Radius of hydrogen / 2R= 5*10^-11/2 = 2.5*10^-11
ANUSH NAYAK
20 Points
6 years ago
 
Ionization energy = 4R = 4*2.2*10^-184* 2.2 * 10^-18 = 13.6 * 1.6 * 10^-19 * z^2=> z = 2R= Radius of hydrogen / 2R= 5*10^-11/2 = 2.5*10^-11
Ashutosh Mittal
13 Points
2 years ago
(i) We know that ionization energy of an hydrogen like atom
is given as
 
E1_, 00 =RchZ2 lu-~
=> E,---,oo = Reh Z2
Here it is given that £ 1..., 00 = 4 rydberg = 4 Reh joule thus, we
have ·
Z2 =4
Z=2
Thus the wavelength emitted when e- makes a transition from
11=2to11=lis
J_ =RZ2 [_!__ __ !] 1', 12 22
=> ";.,-,-r ~ 10967800 X 4 X l ~ , A, 4 * ""32903400
/
~,.,,,.,
· 1'.=304A
(ii) Radius of 11th orbit of a hydrogenic atom having atomic
number Z is given as
,,2
r,,=0.529 x 2 A
HereZ= 2 and 11 = l thus radius of first orbit is
l r=0.529 x 2 A
r=0.2645A

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