Advertisements
Advertisements
प्रश्न
The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?
Advertisements
उत्तर
In n is the quantum number of the highest energy level involved in the transitions, then the total number of possible spectral lines emitted is
`N = (n(n-1))/2`
Third excited state means fourth energy level i.e. n = 4. Here, electron makes transition from n = 4 to n = 1 so highest n is n = 4
Thus, possible spectral lines
`N = (4 (4 -1))/2`
`=(4 xx 3)/2`
= 6
6 is the maximum possible number of spectral lines.
APPEARS IN
संबंधित प्रश्न
How many electrons in an atom may have the following quantum numbers?
n = 4, `m_s = -1/2`
If the velocity of the electron in Bohr’s first orbit is 2.19 × 106 ms-1, calculate the de Broglie wavelength associated with it.
Suppose, the electron in a hydrogen atom makes transition from n = 3 to n = 2 in 10−8 s. The order of the torque acting on the electron in this period, using the relation between torque and angular momentum as discussed in the chapter on rotational mechanics is
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.
The energy of an electron in an excited hydrogen atom is - 3.4 eV. Calculate the angular momentum of the electron according to Bohr's theory. (h = 6.626 × 10-34 Js)
The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass mp, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = mpc/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if mp were 10-6 times the mass of an electron.
An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.
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.
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 ______.
