Question

Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate: (a) the frequency of emission, (b) distance travelled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy.

Solution

Here, $straight lambda space equals space 616 space nm space equals space 616 space cross times space 10 to the power of negative 9 end exponent straight m$
(a) Frequency of emission,
$straight v space equals straight c over straight lambda space equals fraction numerator 3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent over denominator 616 space cross times space 10 to the power of negative 9 end exponent straight m end fraction space equals space 4.87 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent$

(b) Velocity of radiation = $3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent$
$therefore space space space Distance space travelled space in space 30 space straight s space space space space space space space equals space 300 space cross times space 10 to the power of 8 ms to the power of negative 1 end exponent cross times space 30 straight s space equals space 9.0 cross times 10 to the power of 9 straight m$

(c) $straight E space equals space hv space equals space straight h straight c over straight lambda$
$equals space fraction numerator left parenthesis 6.626 space cross times space 10 to the power of negative 34 end exponent Js right parenthesis space cross times space left parenthesis 3.0 space cross times space 10 to the power of 8 space ms to the power of negative 1 end exponent right parenthesis over denominator 6.6 space cross times space 10 to the power of negative 9 end exponent straight m end fraction space equals 32.37 space cross times space 10 to the power of negative 20 end exponent straight J$

(d) Number of quanta in 2J of energy
$equals space fraction numerator 2 over denominator 32.27 space cross times space 10 to the power of negative 28 end exponent end fraction space equals 6.2 space cross times space 10 to the power of 18$

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Structure Of Atom

Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate: (a) the frequency of emission, (b) distance travelled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy.

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