Home
Class 12
PHYSICS
The ratio of the speed of the electrons ...

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

A

`1//2`

B

`2//137`

C

`1//137`

D

`1//237`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the speed of electron in `n^(th)` orbit of atom be `v_(n)`.
We know, `v_(n) = (Ze^(2))/(2epsilon_(0)nh)`
For ground state, n = 1
`v_(1) = e^(2)/(2epsilon_(0) xx 1 xx h)`
`v_(1)/c = (e^(2)/(2 epsilon_(0)h) (1/c))`
`(v_(1)/c) = ((1.6 xx 10^(-19)) xx (1.6 xx 10^(-19)))/(2 xx 8.85 xx 10^(-12) xx 6.63 xx 10^(-34) xx 3 xx 10^(8))`
`(v_(1))/c = 1/137`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • NTA TPC JEE MAIN TEST 60

    NTA MOCK TESTS|Exercise PHYSICS|30 Videos

  • NTA TPC JEE MAIN TEST 63

    NTA MOCK TESTS|Exercise PHYSICS|30 Videos

Similar Questions

Explore conceptually related problems

Calculate the energy of the electron in the ground state of the hydrogen atom.

The speed of light in vacuum is equal to

Knowledge Check

  • The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h and c have their usual meaning in cgs system)

    A
    `2 pi h // e^(2)`
    B
    `e r^(2) h// 2 pi c`
    C
    `e ^(2) c// 2 pi h`
    D
    `2 pi e^(2)// h c`

  • The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h and c have their usual meanings)

    A
    `2pihc//e^(2)`
    B
    `e^(2)h//2pic`
    C
    `e^(2)c//2pih`
    D
    `2pie^(2)//hc`

  • If omega the speed of electron in the nth orbit hydrogen atom, then

    A
    `omega propn^(1//2)`
    B
    `omegaprop(1)/(n)`
    C
    `omega prop(1)/(n^(2))`
    D
    `omegaprop(1)/(n^(3))`

    • Similar Questions

    Explore conceptually related problems

    Hydrogen atom is formod with ono proton and one electron. In ground state, the electron revolves around the proton in an orbit of radius 0.53 angstrom. Find the speed of the electron in the ground state of a hydrogen atom. Speed that we get is usually infinitely large in comparison to the usual speeds and also comparable to the speed of light to a certain extent. Is it all right to assume that the mass of the electron is equal to 9.1 xx 10^(-31) kg? We know that mass changes with speed.

    Find the speed of the electron in the ground state of hddrogen atom. The description of ground state is given in the previous problem.

    What is the exact speed of light in vacuum ?

    The ratio of energy of the electron in ground state of hydrogen to the electron in first excited state of Be^(3+) is

    The speed of an electron in the 4^"th" orbit of hydrogen atom is

    Home
    Profile