Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

OR

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

93219 24448 / 99871 78554

Mon to Sat - 10 AM to 7 PM

a single electron

atom has a nuclear charge +zewhere z is the atomic number and eis the electronic charge it requires 47.2ev to exitethe electron from the second bohrs orbit to third bog=hars orbit fron the above given data solve the following 

(a) what is the atomic number of element 

(b) energy required for transition of electron from the third to fourth bohars orbit is 

(c) the wavelength required to remove the electron from the first bors orbit to infinity

(d) kinetic energy of electron in first bohrs orbit is

Asked by gargpuneet989 28th June 2018, 5:45 PM
Answered by Expert
Answer:
Given:
 
The energy required to excite the electron from the second orbit to the third orbit = 47.2 eV
 
For hydrogen-like atoms,
 
open parentheses straight a close parentheses
Change space in space energy space straight E subscript straight n subscript 2 end subscript minus straight E subscript straight n subscript 1 end subscript equals space straight Z squared straight E subscript 0 open parentheses 1 over straight n subscript 1 squared minus 1 over straight n subscript 2 squared close parentheses space eV

Ionisation space energy space of space hydrogen space atom space straight E subscript 0 space equals space 13.6 space eV

Bohr space Radius space equals space 5.3 cross times 10 to the power of negative 11 end exponent space straight m

Velocity space of space light space equals space 3 cross times 10 to the power of 8 space straight m divided by straight s

increment straight E space equals space straight Z squared space cross times 13.6 open parentheses 1 over 2 squared minus 1 over 3 cubed close parentheses

space 47.2 space equals space straight Z squared space cross times 13.6 open parentheses fraction numerator 9 minus 4 over denominator 36 end fraction close parentheses

space straight Z squared space equals space fraction numerator negative 47.2 cross times 36 over denominator 13.6 cross times 5 end fraction

straight Z squared space equals space 25

straight Z space equals space 5 space

open parentheses straight b close parentheses

Energy space required space for space transition space of space electron space from space the space third space to space fourth space orbit space is comma

straight E subscript 4 minus straight E subscript 3 equals space space straight Z squared straight E subscript 0 open parentheses 1 over straight n subscript 1 squared minus 1 over straight n subscript 2 squared close parentheses space eV

space space space space space space space space space space space equals 5 to the power of 5 cross times 13.6 open parentheses 1 over 3 squared minus 1 over 4 squared close parentheses

space space space space space space space space space space space equals 25 cross times 13.6 open parentheses fraction numerator 16 minus 9 over denominator 144 end fraction close parentheses

space space space space space space space space space space space space equals 16.5 minus 2 space eV

open parentheses straight c close parentheses
The space wavelength space required space to space remove space the space electron space from space the space first space orbit space to space infinity

Energy space required space

straight E subscript infinity minus space straight E subscript 1 space equals space straight Z squared straight E subscript 0 open parentheses 1 over 1 squared minus 1 over infinity squared close parentheses space eV


space space space space space space space space space space space space space space space space equals 25 cross times 13.6 space eV

Wavelenght comma space straight lambda space equals space fraction numerator hc over denominator increment straight E end fraction

space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses 6.5 cross times 10 to the power of negative 34 end exponent close parentheses cross times 3 cross times 10 to the power of 8 over denominator 25 cross times 13.6 space cross times 1.6 cross times 10 to the power of negative 19 end exponent end fraction

space space space space space space space space space space space space space space space space space space space space space space space space equals space 36.4 space cross times 10 to the power of negative 10 space end exponent space
space space space space space space space space space space space space space space
space space space space space space space space space space space space space space space space space space space space space space space space equals space 36.4 space straight A to the power of ring operator

open parentheses straight d close parentheses kinetic space energy space of space electron space in space first space bohrs space orbit space is space numerically space equal space to space the space energy space of space the space orbit

straight E subscript 1 space equals negative straight Z squared straight E subscript 0

therefore KE space equals space 25 cross times 13.6 space cross times 1.6 cross times 10 to the power of negative 19 end exponent space

KE space equals space 544 cross times 10 to the power of negative 19 end exponent space straight J
Answered by Expert 29th June 2018, 11:53 AM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp