Advertisements
Advertisements
प्रश्न
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.
उत्तर १
Energy of incident photon (E) is given by,
`E = ("hc")/lambda`
`= ((6.626xx10^(-34) " Js")(3.0 xx 10^8 " ms"^(-1)))/(150xx10^(-12) " m")`
`= 1.3252 xx 10^(-15)` J
`= 13.252 xx 20^(-16)` J
Energy of the electron ejected (K.E)
`= 1/2 "m"_"e""v"^2`
`=1/2(9.10939xx10^(-31) " kg")(1.5 xx 10^7 " ms"^(-1))^2`
= 10.2480 × 10–17 J
= 1.025 × 10–16 J
Hence, the energy with which the electron is bound to the nucleus can be obtained as:
= E – K.E
= 13.252 × 10–16 J – 1.025 × 10–16 J
= 12.227 × 10–16 J
`= (12.227xx10^(-16))/(1.602xx10^(-19))` eV
`= 7.6 xx 10^3` eV
`(5lambda_0 - 2000)/(4lambda_0 - 20000) = (5.35/2.55)^2 = 28.6225/6.5025`
`(5lambda_0 - 2000)/(4lambda_0- 2000) = 4.40177`
`17.6070lambda_0 - 5lambda_0 = 8803.537- 2000`
`lambda_0 = (6805.537)/12.607`
`lambda_0 = 539.8 "nm"`
`lamda_0 = 540 "nm"`
उत्तर २
Energy of the incident photon= hc/λ = (6.626×10-34 Js×3.0×108 ms-1)/(150×10-12m) = 13.25×10-16 J
Energy of the electron ejected = 1/2 mv2 = 1/2×(9.11×10-31kg)×(1.5×107ms-1)2 = 1.025×10-16 J
Energy with which the electron was bound to the nucleus = 13.25×10-16 J - 1.025×10-16 J
= 12.225×10-16 J = 12.225×10-16/1.602×10-19 eV = 7.63×103 eV
APPEARS IN
संबंधित प्रश्न
What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.
Draw a neat, labelled energy level diagram for H atom showing the transitions. Explain the series of spectral lines for H atom, whose fixed inner orbit numbers are 3 and 4 respectively.
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
if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:
a)`E_k = -E_p"/"2`
b) `E_k = -E_p`
c) `E_k = -2E_p`
d) `E_k = 2E_p`
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (Φ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of λ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
Mention demerits of Bohr’s Atomic model.
If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.
The ratio of the ionization energy of H and Be+3 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 ______.
The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.
Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.
A hydrogen atom in its first excited state absorbs a photon of energy x × 10-2 eV and exited to a higher energy state where the potential energy of electron is -1.08 eV. The value of x is ______.
What is the energy of an electron in stationary state corresponding to n = 2?
The total energy of an electron in the nth orbit of the hydrogen atom is proportional to ______.
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
