A photon of green light has a wavelength of 520 nm. Find the photon's frequency, magnitude of m

A photon of green light has a wavelength of 520 nm. Find...

Key Concepts

Photon Momentum

In quantum mechanics, even though photons are massless, they carry momentum. The magnitude of a photon's momentum is given by the equation p = h/?, which arises from the wave-particle duality of light and underpins many phenomena in quantum physics.

Energy Unit Conversion

Energy can be expressed in various units depending on the context of the analysis. Converting energy from joules to electron volts is a common practice, as 1 electron volt (eV) is defined as 1.602 × 10?¹? joules. This conversion is crucial for comparing and interpreting energy values across different physical settings.

Electromagnetic Wave Properties

Electromagnetic waves are characterized by their wavelength and frequency, which are inversely related through the constant speed of light. This fundamental concept, expressed in the equation c = ??, allows one to determine the frequency when the wavelength is known, or vice versa, and is central to understanding the behavior of light as a wave.

Planck's Constant and Photon Energy

Planck's constant is a pivotal quantity in quantum mechanics, linking the energy of a photon to its frequency via the equation E = hf. This relation shows that energy is quantized and is essential for calculating the energy carried by individual photons.

Transcript

00:01 We have given wavelength here and we have to calculate the frequency momentum and the energy for that given photon okay so now the first part so we have to calculate here the frequency of photon so frequency nu so that is equals to c divided by lambda so c is the speed of light that is 3 multiplying 10 raised to power 8 meter per second divided by 520 nanometer okay so now this is meter per second this is nanometer so this need to convert it into meters so for that instead of nanometer we can write here multiplying 10 raised to power minus minus 9 meter okay so now solving this we will get so this will be 5 .769 okay or let me round this off and this will be 577 5 .77 and now solving all this the power so we will gets 10 raised to power 14 okay so this is in terms of second inverse okay and that is the frequency we have now for second part so magnitude of momentum that can be calculated with the help of de broglie equation by de broglie equation.

01:57 So, now this will be lambda is equals to h divided by mass multiplied by velocity.

02:14 This mass multiplied by velocity that is called momentum.

02:18 Okay.

02:19 So, this can also be written as lambda is equals to h divided by p.

02:25 Okay.

02:25 So, p is for for momentum here okay small p so now this can further be written as momentum okay let me write it here momentum p so that is equals to h divided by lambda so h is the planck constant we have 6 .626 multiplying 10 raised to power minus 34 joule second divided by wavelength that is 520 multiplying 10 raised to power minus 9 meter now this will be equal to okay so dividing this we will get 0 .0127 multiplying solving the powers this will be 10 raised to power minus 25 and now solving the units we will get kilogram meter second inverse okay shifting the decimal we can write 1 .27 multiplying now we are shifting the decimal to right side so the power will be negative okay so that's why this will be 10 raised to power minus 27 kilogram meter second inverse so that is the required momentum for the given wavelength now in the third part we have to calculate the energy so that is given by a plank equation okay so, energy e is equals to h nu...

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