Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given: Ground state energy = −13.6 eV
For a hydrogen atom,
En = `(-13.6)/n^2 eV`
First excited state ⇒ n = 2
E2 = `(-13.6)/2^2`
= `(-13.6)/4`
= −3.4 eV
In the Bohr model:
K.E. = ∣En∣ = 3.4 eV
= 3.4 × 1.6 × 10−19
= 5.44 × 10−19 J
By using de-Broglie relation:
λ = `h/p`
Since,
K.E.= `p^2/(2 m)`
p = `sqrt(2 m K.E.)`
Thus,
λ = `h/sqrt(2 m K.E.)`
= `(6.63 xx 10^-34)/(sqrt(2 xx 9.1 xx 10^-31 xx 5.44 xx 10^-19))`
= 6.66 × 10−10 m
= 6.66 Å
RELATED QUESTIONS
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
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of the hydrogen atom.
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v
State any two Bohr’s postulates and write the energy value of the ground state of the hydrogen atom.
According to Bohr, 'Angular momentum of an orbiting electron is quantized'. What is meant by this statement?
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?
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 ______.
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 ______.
The de Broglie wavelength of an electron in the first Bohr’s orbit of hydrogen atom is equal to ______.
