physics - A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: \lambda_1 = 3650 Å, \lambda_2 = 4047 Å, \lambda_3 = 4358 Å, \lambda_4 = 5461 Å, \lambda_5 = 6907 Å, The stopping voltages, respectively, were measured to be: V_{01} = 1.28 V, V_{02} = 0.95 V V_{03} = 0.74 V, V_{04} = 0.16 V, V_{05} = 0 V Determine the value of Planck’s constant h, the threshold frequency and work function for the material. [Note: You will notice that to get h from the data, you will need to know e (which you can take to be 1.6* 10^{-19} C). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: \lambda_1 = 3650 Å, \lambda_2 = 4047 Å, \lambda_3 = 4358 Å, \lambda_4 = 5461 Å, \lambda_5 = 6907 Å, The stopping voltages, respectively, were measured to be: V_{01} = 1.28 V, V_{02} = 0.95 V V_{03} = 0.74 V, V_{04} = 0.16 V, V_{05} = 0 V Determine the value of Planck’s constant h, the threshold frequency and work function for the material. [Note: You will notice that to get h from the data, you will need to know e (which you can take to be 1.6* 10^{-19} C). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

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physics dual nature of radiation and matter ncrt physics photoelectric effect and wave theory of light photon energy equation einstein's photoelectric equation: energy quantum of radiation relationship between wavelength and frequency photoelectric work function of a material threshold frequency formula measuring planck’s constant using the einstein's photoelectric equation 12th grade

Anonym0us (Student, UG1 Grade)

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Photomultiplier tube - Wikipedia

Photomultiplier tubes members of the class of vacuum tubes, and more specifically vacuum phototubes, are extremely sensitive detectors of light in the ultraviolet ...

For more information, see Photomultiplier tube - Wikipedia

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6.4: The Compton Effect - Physics LibreTexts

Nov 5, 2020 ... In Equation 6.4.1, E is the total energy of a particle, p is its linear momentum, and ... Here the photon's energy Ef is the same as that of a light quantum of frequency f, which we introduced to explain the photoelectric effect: Ef=hf=hcλ. The wave relation that connects frequency f with wavelength λ and speed c ...

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https://chemistry.stackexchange.com/questions/1/why-do-atoms ...

... /164/why-are-there-two-hydrogen-atoms-on-some-periodic-tables 2015-06-20 ... .com/questions/313/mercury-amalgams-and-mercury-compounds 2012-05-14 ... 324/when-simulating-spectral-line-broadening-which-convolution-is-preferred ... /1274/calculating-laser-wavelength-power-to-cause-emission-of-light-in-a-gas ...

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Swetha (last edited 2 years ago) (Student, UG1 Grade)

Given that

Determining the value of Planck’s constant h

Step 1: Finding the frequencies of the different lines of the wavelengths given

Relation between the wavelength and frequency

\upsilon = \frac{c}{\lambda}

Where, speed of light c = 3*10^{8} m/s

Frequency \upsilon_1 = \frac{3*10^{8}}{3650 * 10^{-10}} = 8.22* 10^{14} Hz

\upsilon_2=\frac{3*10^8}{4047*10^{-10}}=7.412*10^{14}\ Hz

\upsilon_3 = \frac{3*10^{8}}{4358 * 10^{-10}} = 6.88 * 10^{14} Hz

\upsilon_4 = \frac{3*10^{8}}{5461 * 10^{-10}} = 5.493 * 10^{14} Hz

\upsilon_5 = \frac{3*10^{8}}{6901 * 10^{-10}} = 4.343 * 10^{14} Hz

Step 2: Make a graph with the frequency and voltage relationship.

Graph:

Step 3: Calculating the Planck’s constant

Energy of proton E=h\upsilon\ -\ \phi

eV=h\upsilon-\phi E=h\upsilon\ =\ \frac{hc}{\lambda}

Where, h - Planck's constant, speed of light c = 3*10^{8} m/s , \phi - work function, and \upsilon - frequency.

V = \frac{h}{e} \upsilon - \phi

Comparing the above equation with equation of straight line y = mx + c

Slope of the line m = \frac{h}{e} ......................(1)

Slope of line from the graph

The slope of the line connecting the two points A (5.493 * 10^{14}, 0.16) and B (8.219 * 10^{14}, 1.28)

Slope of the line = \frac{1.28 - 0.16}{8.219 * 10^{14} - 5.493 * 10^{14}}

Slope of the line = 4.1 * 10^{-15} ............................(2)

From equation (1) and (2)

\frac{h}{e} = 4.1 * 10^{-15}

h = 4.1 * 10^{-15} * 1.6 * 10^{-19}

h = 6.4 * 10^{-34} Js

Hence, Planck’s constant h = 6.4 * 10^{-34} Js

Step 4: Finding the work function

Observation from the graph:

The obtained curve is a straight line, as can be shown. It touches the frequency-axis at 5.4 * 10^{14} Hz, which is the

material's threshold frequency ( \upsilon_0 ). A frequency less than the threshold frequency corresponds to point H. As a result,

the \lambda_5 line produces no photoelectric emission, and thus no stopping voltage is needed to stop the current.

Relation between work function and frequency

\phi = h \upsilon_0

\phi = 6.4 * 10^{-34} * 5.4 * 10^{14}

\phi = 3.38 * 10^{-19} J

\phi = 2 ev

Therefore, work function \phi=2eV