Question

In hydrogen atom, the de Broglie wavelength of an
electron in the second Bohr orbit is
[Given that Bohr radius, a, = 52.9 pm]

(1) 105.8 pm
(2) 211.6 pm
(3) 211.6 n pm
(4) 52.9 n pm​

Answer 1

QUESTION :-

In hydrogen atom , the debroglie wavelength of an electron in the second bohr orbit is [Given that the radius of first Bohr orbit is 52.9 pm ]

(1) 105.8 pm

(2) 211.6 pm

(3) 211.6π pm

(4) 52.9π pm

GIVEN :-

• An electron is present in second bohr orbit of hydrogen

TO FIND :-

• Debroglie-wavelength of the electron in second bohr orbit of hydrogen

SOLUTION :-

Radius of nᵗʰ orbit in pm is given by

$\large\rm {\bold{\boxed{ \bigstar{ | \: r_n\:=\:\frac{n^2}{z}\times\:52.9 \: pm |}}}}$

Where ,

• rₙ is Radius of nᵗʰ orbit
• n is number of the orbit
• z is atomic Number

we want the Radius of the Second bohr orbit in hydrogen ,

so ,

• Z = 1
• n = 2

$: \implies \: r_{2} \: = \frac{ ({2})^{2} }{1} \times 52.9 \: pm\\ \\ : \implies \: r_{2} \: = \frac{4}{1} \times 52.9 \: pm\\ \\ : \implies \: r_{2} \: = 4 \times 52.9 \: pm\\ \\ : \implies {\bold {\boxed {\: r_{2} \: = 211.6 \: pm}}}$

Relation between bohr theory and debroglie theory is given by ,

$\large\rm {\bold{\boxed{ \bigstar{ | n \lambda = 2\pi r |}}}}$

Where ,

• n is orbit number or Number of waves
• λ is wavelength
• r is radius

$: \implies \: (2)( \lambda) \: = 2 \times \: \pi \times 211.6 \: pm \\ \\ : \implies \lambda \: = 211.6 \pi \: \: pm$

$\large \dag { \: \: Hence ,\: option(c) \: is \: correct}$

ADDITIONAL INFO :-

★ Debroglie wavelength when mass and velocity are given is given by ,

$\large \underline{ \bold {\boxed { \lambda \: = \frac{h}{mv} }}}$

Where ,

• h is planck's constant
• m is mass
• v is velocity

★ Debroglie wavelength when mass and kinetic enery are given is given by,

$\large\underline\bold{\boxed{\lambda\:=\:\frac{h}{\sqrt{2mKE}}}}$

Where ,

• h is planck's constant
• m is mass
• KE is kinetic energy

Answer 2

Answer:

211.6 pie pm

Explanation:

pls find the solution in the image attached

hope it helps