Correct Answer - Option 3 : All the above
CONCEPT:
- The kinetic energy of the electron in an orbit is given by
\(⇒ KE = \frac{1}{2}mV^{2} = \frac{1}{2} m \times \frac{e ^{2}}{4\pi \epsilon_{0}mr} =\frac{e^{2}}{8\pi\epsilon_{0}mr}\)
- The potential energy of an electron in an orbit is given by
\(⇒ U = -\frac{e^{2}}{4\pi\epsilon_{0}r}\)
- The total energy of the electron is given by
⇒ T = KE + U
\(⇒ T = \frac{e^{2}}{8\pi\epsilon_{0}r} - \frac{e^{2}}{4\pi\epsilon_{0}r} = -\frac{e^{2}}{8\pi \epsilon_{0}r}\)
Where e= charge, r = orbital radius, T = Total energy
EXPLANATION:
- The total energy of an electron in an atom is given by
\(⇒ T = -\frac{e^{2}}{8\pi \epsilon_{0}r}\)
- By analyzing the above equation it is clear that the total energy is inversely proportional to the distance, which in turn means that
- As the value of r changes the value of T changes, which justifies statement 4
- As the value of r increases the value of T increases, which justifies statement 3. [ Kindly note the negative sign in the equation of T, \(T = -\frac{e^{2}}{8\pi \epsilon_{0}r}\)]
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By giving an amount of energy that equal to the energy of an electron in an atom the electron can be released from it.
- Since the energy of an electron in an atom is \( T = -\frac{e^{2}}{8\pi \epsilon_{0}r}\)if we gave energy \( E = +\frac{e^{2}}{8\pi\epsilon_{0}r}\)then the electron can be released from the atom. Hence, statement 2 is correct
- The energy of an electron in an atom is \(T = -\frac{e^{2}}{8\pi \epsilon_{0}r}\) , by analyzing the equation means the electron is having negative energy, which in turn means the electron can't escape from the atom. Hence, statement 1 is correct
- The option which states all the statement is correct is the answer, Hence, option 3 is the answer
- Options 1, 2, and 3 doesn't contain all the statements. Hence these options are incorrect
