Advertisements
Advertisements
Question
Radiation coming from transition n = 2 to n = 1 of hydrogen atoms falls on helium ions in n = 1 and n = 2 states. What are the possible transitions of helium ions as they absorbs energy from the radiation?
Advertisements
Solution
Energy of radiation (E) from the hydrogen atom is given by
`E = 13.6 (1/n_1^2 - 1/n_2^2 )`
Hydrogen atoms go through transition, n = 1 to n = 2.
The energy released is given by
`E = 13.6 (1/1-1/4)`
`= 13.6xx3/4 = 10.2 eV`
For He,
Atomic no, Z = 2
Let us check the energy required for the
transition in helium ions from n = 1 to n = 2.
`therefore` n1 =1 to n2 = 2
Energy (E1) of this transition is given by
`E_1 = Z^2 13.6 (1/n_1^2 - 1/n_2^2)`
= `4xx13.6(1 - 1/4)`
= 40.8 eV
E1 > E,
Hence, this transition of helium ions is not possible.
Let us check the energy required for the transition in helium ion from n = 1 to n = 3.
`therefore n_1 =1` to `n_2 = 3`
Energy (E2) for this transition is given by
E2 =`Z^2 xx 13.6 (1/n_2^2 - 1/n_1^2)`
= `4xx13.6xx(1/1- 1/9)`
= 48.3 eV
It is clear that E2 > E.
Hence, this transition of helium ions is not possible.
Similarly, transition from n1 = 1 to n2 = 4 is also not possible.
Let us check the energy required for the transition in helium ion from n = 2 to n=3
∴ n1 = 2 to n2 = 3
Energy (E3) for this transition is given by
`E_3 = 13.6xx4(1/4 - 1/9)`
= `(20xx13.6)/36 = 7.56 ev`
Let us check the energy required for the transition in helium ion from n = 2 to n = 3.
∴ n1 = 2 to n2 = 4
Energy (E_4) for this transition is given by
`E_4 = 13.6xx4 (1/4 - 1/16)`
`= 13.6xx3/4 = 10.2 eV`
We find that
E3 < E
E4 = E
Hence, possible transitions are from n = 2 to n = 3 and n = 2 to n = 4.
APPEARS IN
RELATED QUESTIONS
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
- n = 0, l = 0, ml = 0, ms = + ½
- n = 1, l = 0, ml = 0, ms = – ½
- n = 1, l = 1, ml = 0, ms = + ½
- n = 2, l = 1, ml = 0, ms = – ½
- n = 3, l = 3, ml = –3, ms = + ½
- n = 3, l = 1, ml = 0, ms = + ½
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.
A filter transmits only the radiation of wavelength greater than 440 nm. Radiation from a hydrogen-discharge tube goes through such a filter and is incident on a metal of work function 2.0 eV. Find the stopping potential which can stop the photoelectrons.
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
State any two Bohr’s postulates and write the energy value of the ground state of the hydrogen atom.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
For an electron in the second orbit of hydrogen, what is the moment of momentum as per the Bohr's model?
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 simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.
The Bohr model for the spectra of a H-atom ______.
- will not be applicable to hydrogen in the molecular from.
- will not be applicable as it is for a He-atom.
- is valid only at room temperature.
- predicts continuous as well as discrete spectral lines.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.
State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to `(1/"n")`.
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ1/λ2, of the photons emitted in this process is ______.
The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is ______.
In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.
An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.
State the Bohr's postulate of angular momentum of an electron.
