Advertisements
Advertisements
प्रश्न
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10−27 kg. (c) Find the kinetic energy of recoil of the atom.
Advertisements
उत्तर
Given:
Wavelength of light emitted by hydrogen, λ = 656.3 nm
Mass of hydrogen atom, m = 1.67 × 10−27 kg
(a) Momentum (P) is given by
P =`h/lamda`
Here,
h = Planck's constant
λ = Wavelength of light
`therefore p = (6.63xx10^-34)/(656.3 xx 10^-9)`
p = 0.01×10-25
p =1 × 10-27 kgm/s
(b) Momentum, p = mv
Here,
m = Mass of hydrogen atom
v = Speed of atom
`therefore 1xx10^-27 = (1.67xx10^-27)xxU`
`rArr v = 1/1.67 = 0.598 = 0.6 m/s`
(c) Kinetic energy (K) of the recoil of the atom is given by
`K = 1/2mv^2`
Here,
m = Mass of the atom
v = Velocity of the atom
`therefore K = 1/2 xx (1.67xx10^-27)xx(0.6)^2 J`
`K = (0.3006xx10^-27)/(1.6xx10^-19)eV`
`K = 1.9 xx 10^-9 ev`
APPEARS IN
संबंधित प्रश्न
Obtain an expression for the radius of Bohr orbit for H-atom.
Calculate the radius of second Bohr orbit in hydrogen atom from the given data.
Mass of electron = 9.1 x 10-31kg
Charge on the electron = 1.6 x 10-19 C
Planck’s constant = 6.63 x 10-34 J-s.
Permittivity of free space = 8.85 x 10-12 C2/Nm2
Calculate the energy required for the process
\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]
The ionization energy for the H atom in the ground state is 2.18 ×10–18 J atom–1
Write the expression for Bohr’s radius in hydrogen atom ?
The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.
Evaluate Rydberg constant by putting the values of the fundamental constants in its expression.
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.
What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
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 ______.
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.
The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.
According to Bohr atom model, in which of the following transitions will the frequency be maximum?
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 ______.
A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ______.
(Given, Planck's constant = 6.6 × 10-34 Js)
The radius of the nth orbit in the Bohr model of hydrogen is proportional to ______.
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
Calculate the radius of the second orbit of He+.
Which expression gives the quantised angular momentum of the orbiting electron?
