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Important problems of Bohr's Radius (In Hindi)
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In this lesson we will learn about some important problems based on the concept of Bohr's radius for IIT-JEE students

Niranjay Kumar Dwivedi
(N.K.D.Sir) is a Complete Chemistry faculty for IIT~JEE, and NEET examination. with more then 8 year of Teaching experience

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Bdiya sir g

2. If the radius of first Bohr orbit is x, then de Broglie wavelength of electron in 3rd orbit is nearly. (A)2x (C)9x (B) 6X Solution: rn-nao, ro n2 Also mvrn = 2n 2h 2 mvr3 = mv = mv

3. The radiation is emitted when a hydrogen atom goes from a high energy state to a lower energy state. The wavelength of one line an visible region of atomic spectrum of hydrogen is 6.5 x 10-9 m. Energy difference between the two states is 3.0 x10-17J (B) 1.0 x1018J 5.0 x10-10 (D) 6.5 x10-7J Solution: hv#, 6626.53103-10s #3 x 10-17, Solution: = hv= he = 6.5%10.9 -3x10-17J

4. Calculate the ratio of the radius of Li*2 ion in 3rd energy level to that of He+ ion in 2nd energy level Solution: r c (for Li-) (for He*) 2 3 3) 2

5. Which is larger, an Het ion with an electron in an orbit with n- 3 or Li2 ion with an electron in an orbit with n 5? Solution: Radius of the nth Bohr's orbit of the species of atomic number Z is given by n'ao Where ap( 0.529 ) is called Bohr's radius. 25ao i) T,(Li2 ,Z-38.33a

6. The wave number of the first Balmer line in the hydrogen spectrum is 15200 cm', Calculate the wavelength of the first Lyman line in the spectrum of He, Li* Solution --RZ'I _32 1 1 R-15200x36cm Z-1 for hydrogen For He ,v4x1200 2C : Wavelength of the first Lynan lin8320 cm 3046x10 cm-304.6A Similarly for Li, 9x15200x cm738720cm and -1.354 x 10-6 crn-1 35.4 A 36 1 51 1 din-i (Lyrnan Series) = 328320 cm"! cm3.046x 10 c304.6 A 328320 36 3-1

7. (i) What is the energy and wavelength o photons of frequency 3.4 MHz? Also calculate the energy per mole o photons of the same wavelength Solutionv 3.4 MH 3.4x10 H 3.4x 10 s 10 88.2m v 3.4x106 s Energy, E 6.626x10 x3.4x10J 1.356x10 J Energy per mole of photon 6.02x10 x2253x10 J mol -1.356x10 J mol What is the wavelength of he first line in Paschen series of the hydrogen spectrum? Solution 15200cm Paschen series.z-1 109737 x 0.0486 5334 cm.. 2-1.875x104cm