Advertisements
Advertisements
Question
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
Solution
The dimensions of ε0 can be derived from the formula given below:
`a = (epsilon_0h^2)/(pime^2) = (A^2T^0(ML^2 T^-1)^2)/(L^2ML^-2 (AT)^2)`
`=(M^2L^2T^-2)/(M^2L^3T^-2) = L`
Clearly, a0 has the dimensions of length.
APPEARS IN
RELATED QUESTIONS
State Bohr’s third postulate for hydrogen (H2) atom. Derive Bohr’s formula for the wave number. Obtain expressions for longest and shortest wavelength of spectral lines in ultraviolet region for hydrogen atom
State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of Hα line. [Given: Rydberg constant R = 1.03 × 107 m−1]
The energy associated with the first orbit in the hydrogen atom is - 2.18 × 10-18 J atom-1. What is the energy associated with the fifth orbit?
Calculate the radius of Bohr’s fifth orbit for hydrogen atom
How many electrons in an atom may have the following quantum numbers?
n = 4, `m_s = -1/2`
The light emitted in the transition n = 3 to n = 2 in hydrogen is called Hα light. Find the maximum work function a metal can have so that Hα light can emit photoelectrons from it.
If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.
Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.
The energy of an electron in hth orbit of hydrogen atom is –13.6/n2ev energy required to excite the electron from the first orbit to the third orbit is
For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true ______.
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.
A 100 eV electron collides with a stationary helium ion (He+) in its ground state and exits to a higher level. After the collision, He+ ions emit two photons in succession with wavelengths 1085 Å and 304 Å. The energy of the electron after the collision will be ______ eV.
Given h = 6.63 × 10-34 Js.
What is the energy of an electron in stationary state corresponding to n = 2?
An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.
Write the ionisation energy value for the hydrogen atom.
The energy of an electron in the nth orbit of the hydrogen atom is En = -13.6/n2eV. The negative sign of energy indicates that ______.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
