Search any question & find its solution
Question:
Answered & Verified by Expert
Neon gas is generally used in the sign boards. If it emits strongly at \(616 \mathrm{~nm}\), calculate
(a) the frequency of emission
(b) distance traveled by this radiation in \(30 \mathrm{~s}\)
(c) energy of quantum and
(d) number of quanta present if it produces \(2 \mathrm{~J}\) of energy.
(a) the frequency of emission
(b) distance traveled by this radiation in \(30 \mathrm{~s}\)
(c) energy of quantum and
(d) number of quanta present if it produces \(2 \mathrm{~J}\) of energy.
Solution:
2667 Upvotes
Verified Answer
\(\lambda=616 \mathrm{~nm}=616 \times 10^{-9} \mathrm{~m}\)
(a) Frequency,
\(v=\frac{\mathrm{c}}{\lambda}=\frac{3.0 \times 10^8 \mathrm{~ms}^{-1}}{616 \times 10^{-9} \mathrm{~m}}=4.87 \times 10^{14} \mathrm{~s}^{-1}\)
(b) Velocity of the radiation \(=3.0 \times 10^8 \mathrm{~ms}^{-1}\)
\(\therefore\) Distance travelled in \(30 \mathrm{~s}\)
\(=30 \mathrm{~s} \times 3 \times 10^8 \mathrm{~ms}^{-1}=9.0 \times 10^9 \mathrm{~m}\)
(c) \(\mathrm{E}=h v=h \frac{\mathrm{c}}{\lambda}\)
\(=\frac{\left(6.626 \times 10^{-34} \mathrm{Js}\right) \times 3.0 \times 10^8 \mathrm{~ms}^{-1}}{616 \times 10^{-9} \mathrm{~m}}=32.27 \times 10^{-20} \mathrm{~J} \text {. }\)
(d) No. of quanta in \(2 \mathrm{~J}\) of energy
\(=\frac{2}{32.27 \times 10^{-20}}=6.2 \times 10^{18}\)
(a) Frequency,
\(v=\frac{\mathrm{c}}{\lambda}=\frac{3.0 \times 10^8 \mathrm{~ms}^{-1}}{616 \times 10^{-9} \mathrm{~m}}=4.87 \times 10^{14} \mathrm{~s}^{-1}\)
(b) Velocity of the radiation \(=3.0 \times 10^8 \mathrm{~ms}^{-1}\)
\(\therefore\) Distance travelled in \(30 \mathrm{~s}\)
\(=30 \mathrm{~s} \times 3 \times 10^8 \mathrm{~ms}^{-1}=9.0 \times 10^9 \mathrm{~m}\)
(c) \(\mathrm{E}=h v=h \frac{\mathrm{c}}{\lambda}\)
\(=\frac{\left(6.626 \times 10^{-34} \mathrm{Js}\right) \times 3.0 \times 10^8 \mathrm{~ms}^{-1}}{616 \times 10^{-9} \mathrm{~m}}=32.27 \times 10^{-20} \mathrm{~J} \text {. }\)
(d) No. of quanta in \(2 \mathrm{~J}\) of energy
\(=\frac{2}{32.27 \times 10^{-20}}=6.2 \times 10^{18}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.