Alaser pulse with wavelength 525 nm contains 4.40 mj of energy. how many photons are in the laser pulse
The laser pulse in this question has a wavelength of . To solve this problem, we first have to calculate the energy of a single photon in the laser pulse. The equation for calculating the energy of a single photon of an electromagnetic wave is where is the speed of light, is planks constant and is the wave length of the photons. For this problem, , and . We use these values to calculate the energy of the photon as shown below, Now that we know the energy for a single photon, we will divide the total energy given by the energy of one photon to get the number of photons in the pulse. The number of photons is calculated as shown below, . There are photons.
1.04 × 10¹⁶ photons Explanation: 1) Data: E = 3.85mJj (mili joules) = 3.85×10⁻³ J λ = 532 nm = 532 × 10⁻⁹ mnumber of photons ? 2) Physical principles a) The energy of a photon is given by the equation E = hν. Where: h is Planck’s constant 6.62607004 × 10⁻³⁴ J×sν is the freguency of the light b) The wavelength, λ, and the frequency, are related by the equation: ν = c / λ, where c is the speed of light at vacuum, approximately 3.0 × 10⁸ m/s 3) Solution: ν = c / λ = 3.0 × 10⁸ m/s / (538 nm) × 10⁹ nm/m = 5.576×10¹⁴ HzE = hν = 6.62607004 × 10⁻³⁴ J×s s × 5.576×10¹⁴ Hz = 3.69 × 10 ⁻¹⁹ JDivide the total energy by the energy of one photon to find the number of photons: 3.85×10⁻³ J / 3.69 × 10 ⁻¹⁹ J-photon = 1.04 × 10¹⁶ photons ← answer
– Solution:- First of we calculate the energy of the laser pulse for it’s given wavelength which actually the energy in joule per photon. After this the given energy value is divided by the calculated energy to find out the number of photons. The calculations are done as: For energy calculations the equation used is: where, E is energy, h is planck’s constant and is the wavelength. The values of the constants are as follows: wavelength is given as 550 nm. We need to convert it to m. Let’s plug in the values in the equation to calculate E: This is the energy for one photon. The given energy value is 4.40 mJ that is . let’s divide this value by the calculated value to get the number of photons as: = So, there would be photons in the laser pulse.
Given: Wavelength (λ) of the laser pulse = 545 nm = 5.45 * 10⁻⁹ m Total energy of pulse = 4.85 mJ To determine: The number of photons in the laser of a given energy Explanation: Energy per photon (E) = hc/λ where h = planck’s constant = 6.626 *10⁻³⁴ Js C = speed of light = 3*10⁸ m/s λ = wavelength E = 6.626 *10⁻³⁴ Js* 3*10⁸ms-1 /5.45 * 10⁻⁹ m = 3.65 * 10⁻¹⁹ J Now, # photons = total energy/Energy per photon = 4.85 * 10⁻³ J* 1 photon / 3.65 * 10⁻¹⁹ J = 1.32 * 10¹⁶ photons Ans: the laser pulse contains 1.32 * 10¹⁶ photons
The number of photons that are in the laser pulse is about : 1.03 × 10¹⁶ photons Further explanation The term of package of electromagnetic wave radiation energy was first introduced by Max Planck. He termed it with photons with the magnitude is: E = Energi of A Photon ( Joule ) h = Planck’s Constant ( 6.63 × 10⁻³⁴ Js ) f = Frequency of Eletromagnetic Wave ( Hz ) The photoelectric effect is an effect in which electrons are released from the metal surface when illuminated by electromagnetic waves with large enough of radiation energy. E = Energi of A Photon ( Joule ) m = Mass of an Electron ( kg ) v = Electron Release Speed ( m/s ) Ф = Work Function of Metal ( Joule ) q = Charge of an Electron ( Coulomb ) V = Stopping Potential ( Volt ) Let us now tackle the problem! Given: wavelength = λ = 532 nm = 532 × 10⁻⁹ m energy = E = 3.85 mJ = 3.85 × 10⁻³ J Asked: number of photons = N = ? Solution: Learn morePhotoelectric Effect : Statements about the Photoelectric Effect : Rutherford model and Photoelecric Effect : Photoelectric Threshold Wavelength : Answer details Grade: High School Subject: Physics Chapter: Quantum Physics
Answer 6
Wavelength is the
ratio of speed of light and frequency: wavelength = speed of
light / frequency where frequency is: (c
is speed of light)
freq = c / wavelength = 3E8/550E-9 = 5.45E14 Hz We know that photons have energy E = hf = 6.626E-34 Js * 5.45E14
Hz = 3.61 E-19 J Therefore if it has 4.40 mJ of energy, the pulse has: 4.40E-3/3.61E-19 = 1.22E16 photons
Answer 7
The Planck-Einstein equation isE = (hc)/λwherec = 3 x 10⁸ m/s, the velocity of light The energy per photon ise = fhwhere f = c/λ = 3 x 10⁸/520 x 10⁻⁹ = 5.7692 x 10¹⁴ 1/s The number of photons isE/e = c/(fλ) = (3 x 10⁸)/[(5.7692 x 10¹⁴)*(520 x 10⁻⁹)] = 1 1
E = hc/λwhereħ is Planck’s constant = 6.626×10⁻³⁴ J·s c is the speed of light = 3×10⁸ m/s λ is the wavelength The wavelength is given to be 540 nm or also equivalent to 540×10⁻⁹ m. Substituting the values,E = (6.626×10⁻³⁴ J·s )(3×10⁸ m/s )/(540×10⁻⁹ m)E = 1.681×10⁻¹⁹ J/photon The total energy is given to be 4.85 mj or also equal to 4.85×10⁻³ J. Thus, Number of Photons = 4.85×10⁻³ J/1.681×10⁻¹⁹ J/photonNumber of Photons = 1.32×10¹⁶
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