question_answer

Define the Q value of a nuclear process. When can a nuclear process not proceed spontaneously?

If both the number of protons and the number of neutrons are conserved in a nuclear reaction, in what way is mass converted into energy (or vice-versa) in a nuclear relation?

Or

Using Bohr's postulates, derive the expression for the frequency of radiation emitted when electron is hydrogen atom undergoes transition from higher energy state (quantum number \[{{n}_{i}}\]) to the lower state \[({{n}_{f}}).\]

When electron in hydrogen atom jumps from energy state \[{{n}_{i}}=4\] to \[{{n}_{f}}=3,\] identify the spectral series to which the emission lines belong.

Answer:

The Q-value of a nuclear process refers to the energy release in the nuclear process which can be determined using Einstein's mass energy relation \[E=m{{c}^{2}}.\] The Q-value is equal to the difference of mass of products and reactants multiplied by square of velocity of light. The nuclear process does not proceed spontaneously when Q-value of a process is negative or sum of masses of product is greater than sum of masses of reactant. Since, mass defect occurs in nucleus which converts into energy as per Einstein's mass energy relation \[E=m{{c}^{2}}\] and produces binding energy. This energy binds nucleons together due to nuclear forces inspite of repulsive Coulombian forces. Or According to Bohr, energy is radiated in the form of a photon when the electron of an excited hydrogen atom returns from higher energy state to the lower energy state. So, energy is radiated in the form of a photo when electron jumps from higher energy orbit \[(n={{n}_{i}})\] to lower energy orbit  \[(n={{n}_{f}}),\] \[{{n}_{i}}>{{n}_{f}}\] The energy of the emitted photon is given by             \[hv={{E}_{{{n}_{i}}}}-{{E}_{{{n}_{i}}}}\] Energy of nth orbit, \[{{E}_{n}}=\frac{-m{{e}^{4}}}{8{{h}^{2}}\varepsilon _{0}^{2}{{n}^{2}}}\] \[\therefore \]      \[hv=-\frac{m{{e}^{4}}}{8\varepsilon _{0}^{2}n_{i}^{2}{{h}^{2}}}-\left( -\frac{m{{e}^{4}}}{8{{h}^{2}}\varepsilon _{0}^{2}n_{f}^{2}} \right)\] When electron jumps from n = 4 to n = 3 state, the spectral series is called Paschen series.