Advertisements
Advertisements
Questions
An electron in hydrogen atom stays in its second orbit for 10−8 s. How many revolutions will it make around the nucleus at that time?
An electron in hydrogen atom stays in its second orbit for 10−8 s. How many revolutions will it make around the nucleus at that time?
[Given: e = 1.6 × 10-19 C, m = 9.1 × 10-31 kg]
Solution
z = 1, m = 9.1 × 10-31 kg, e = 1.6 × 10-19 C,
ε0 = 8.85 × 10-12 C2 / N⋅m2, h = 6.63 × 10-34 J⋅s
n = 2, t = 10-8s
The periodic time of the electron in a hydrogen atom,
T = `(4ε_0^2h^3n^3)/(pime^4)`
= `((4)(8.85 × 10^-12)(6.63 × 10^-34)^3(8))/((3.142)(9.1 × 10^-31)(1.6 × 10^-19)^4)`
= `((4)(8.85)^2(6.63)^3(8))/((3.142)(9.1)(1.6)^4)xx10^-19 s`
= 3.898 × 10-16 s
Let N be the number of revolutions made by the electron in time t. Then, t = NT
∴ N = `t/T`
= `10^-8/(3.898 xx 10^-16)`
= 2.565 × 107
RELATED QUESTIONS
Write symbolically the nuclear β+ decay process of `""_6^11C` Is the decayed product X an isotope or isobar of (`""_6^11C`)? Given the mass values m (`""_6^11C`) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.
Is the nucleus formed in the decay of the nucleus `""_11^22Na`, an isotope or isobar?
Obtain the binding energy (in MeV) of a nitrogen nucleus `(""_7^14"N")`, given `"m"(""_7^14"N")` = 14.00307 u.
Obtain the binding energy of the nuclei `""_26^56"Fe"` and `""_83^209"Bi"` in units of MeV from the following data:
`"m"(""_26^56"Fe")` = 55.934939 u
`"m"(""_83^209"Bi")`= 208.980388 u
The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei `""_20^41"Ca"` and `""_13^27 "Al"` from the following data:
`"m"(""_20^40"Ca")` = 39.962591 u
`"m"(""_20^41"Ca")` = 40.962278 u
`"m"(""_13^26"Al")` = 25.986895 u
`"m"(""_13^27"Al")` = 26.981541 u
Consider the fission of `""_92^238"U"` by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are `""_58^140"Ce"` and `""_44^99"Ru"`. Calculate Q for this fission process. The relevant atomic and particle masses are
`"m"(""_92^238"U")` = 238.05079 u
`"m"(""_58^140"Ce")` = 139.90543 u
`"m"(""_44^99"Ru")` = 98.90594 u
What is meant by the terms half-life of a radioactive substance and binding energy of a nucleus?
What is the significance of binding energy per nucleon of a nucleus of a radioactive element?
Define half-life of a radioactive substance
Use this graph to explain the release of energy in both the processes of nuclear fusion and fission.
What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number ‘A’ lying 30 < A < 170?
Is it easier to take out a nucleon (a) from carbon or from iron (b) from iron or from lead?
If the nucleons of a nucleus are separated from each other, the total mass is increased. Where does this mass come from?
In which of the following decays the atomic number decreases?
(a) α-decay
(b) β+-decay
(c) β−-decay
(d) γ-decay
Find the binding energy per nucleon of `""_79^197"Au"` if its atomic mass is 196.96 u.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
Which property of nuclear force explains the constancy of binding energy per nucleon `((BE)/A)` for nuclei in the range 20< A < 170 ?
What is the minimum energy which a gamma-ray photon must possess in order to produce electron-positron pair?
Binding energy per nucleon for helium nucleus (2 He) is 7.0 MeV Find value of mass defect for helium nucleus
Calculate mass defect and binding energy per nucleon of `"_10^20 Ne`, given
Mass of `"_10^20 Ne= 19.992397` u
Mass of `"_0^1H = 1.007825` u
Mass of `"_0^1n = 1.008665` u
In a nuclear reactor, what is the function of:
(i) The moderator
(ii) The control rods
(iii) The coolant
Sketch a graph showing the variation of binding energy per nucleon of a nucleus with its mass number.
The figure shows the plot of binding energy (BE) per nucleon as a function of mass number A. The letters A, B, C, D, and E represent the positions of typical nuclei on the curve. Point out, giving reasons, the two processes (in terms of A, B, C, D, and E ), one of which can occur due to nuclear fission and the other due to nuclear fusion.
Calculate the binding energy of an alpha particle given its mass to be 4.00151 u.
In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are\[\ce{_12^24Mg}\](23.98504 u), \[\ce{_12^25Mg}\] (24.98584 u), and \[\ce{_12^26Mg}\] (25.98259 u). The natural abundance of \[\ce{_12^24Mg}\] is 78.99% by mass. Calculate the abundances of other two isotopes.
Determine the binding energy per nucleon of the americium isotope \[\ce{_95^244Am}\], given the mass of \[\ce{_95^244Am}\] to be 244.06428 u.
A body's centre of mass
Mx and My denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a β– decay is Q1 and that for a β+ decay is Q2. If m e denotes the mass of an electron, then which of the following statements is correct?
Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into `p + bare + barν`. If one of the neutrons in Triton decays, it would transform into He3 nucleus. This does not happen. This is because ______.
Heavy stable nucle have more neutrons than protons. This is because of the fact that ______.
The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e′: F = `1/(4πε_0) e^('2)/r` estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.
Find the binding energy of a H-atom in the state n = 2
Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
Calculate the binding energy of an alpha particle in MeV. Given
mass of a proton = 1.007825 u
mass of a neutron = 1.008665 u
mass of He nucleus = 4.002800 u
1u = 931 MeV/c2
State the significance of binding energy per nucleon.
Which of the following quantities is a measure of stability of nucleus?
Calculate the values of x and y in the following nuclear reaction.
\[\ce{^227_89Ac -> ^211_82Pb + x[^4_2He]+ y[^0_-1e]}\]
What is binding energy of nucleus?
What is meant by “binding energy per nucleon” of a nucleus?
