Question

Assuming that the smallest measurable wavelength in an experiment is 0.610 fm (femtometers), what is the maximum mass of an object traveling at 199 m·s–1 for which the de Broglie wavelength is observable?.

Answer 1

1 fm = 1.0 × 10-15 meters 
so
0.610  fm x (1.0x10^-15 m / 1 fm)
                   = 6.1x10^-16 m
so the formula is
λ = h / mu 
so,
as we know mass value so by putting
m = (6.626*10^-34)/(6.1*10^-16*199)
    =(6.626*10^-34)/(1213.96*10^-16)
    = 5.45 x 10^ -21

Answer 2

The maximum mass of the object is about 5.46 × 10⁻²¹ kg

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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:

$\large {\boxed {E = h \times f}}$

E = Energi of A Photon ( Joule )

h = Planck's Constant ( 6.63 × 10⁻³⁴ Js )

f = Frequency of Eletromagnetic Wave ( Hz )

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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.

$\large {\boxed {E = \frac{1}{2}mv^2 + \Phi}}$

$\large {\boxed {E = qV + \Phi}}$

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!

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This problem is about De Broglie's wavelength.

Given:

speed of object = v = 199 m/s

wavelength = λ  = 0.610 fm = 6.1 × 10⁻¹⁶ m

Planck's constant = h = 6.63 × 10⁻³⁴ Js

Asked:

mass of the object = m = ?

Solution:

$\lambda = \frac{h}{mv}$

$6.1 \times 10^{-16} = \frac{6.63 \times 10^{-34}}{m \times 199}$

$\large {\boxed {m \approx 5.46 \times 10^{-21} \texttt{ kg}} }$

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Learn more

• Photoelectric Effect : brainly.com/question/1408276

• Statements about the Photoelectric Effect : brainly.com/question/9260704

• Rutherford model and Photoelecric Effect : brainly.com/question/1458544
• Photoelectric Threshold Wavelength : brainly.com/question/10015690

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Answer details

Grade: High School

Subject: Physics

Chapter: Quantum Physics