Respuesta :
293 grams
The formula for the wavelength of a massive particle is
λ = h/p
where
λ = wavelength
h = Plank constant (6.626070040Ă—10^â’34 J*s)
p = momentum (mass times velocity)
So let's solve for momentum and from there get the mass
λ = h/p
λp = h
p = h/λ
Substitute known values and solve
p = 6.626070040Ă—10^â’34 J*s/3.45Ă—10^-34 m
p = 1.92 J*s/m
Since momentum is the product of mass and velocity, we have
p = M * V
p/V = M
So substitute again, and solve.
p/V = M
1.92 J*s/m / 6.55 m/s = M
1.92 kg*m/s / 6.55 m/s = M
1.92 kg*m/s / 6.55 m/s = M
0.293 kg = M
So the mass is 293 grams
The mass of the ball with a wavelength of [tex]3.45 \times {10^{ - 34}}\;{\text{m}}[/tex] and a velocity of 6.55 m/s is[tex]\boxed{{\text{293 g}}}[/tex].
Further explanation:
de Broglie wavelength:
The de Broglie equation is used to calculate the unknown value from the known values of the two other parameters. It is specially applied to neutral atoms, elementary particles, and molecules. The de Broglie equation for a ball is as follows:
[tex]\lambda =\frac{{\text{h}}}{{{\text{mv}}}}[/tex] …… (1)
Here,
m is the mass of ball.
h is the Planck’s constant.
[tex]\lambda[/tex] is the de Broglie wavelength of ball.
v is the velocity of ball.
Rearrange equation (1) to calculate the mass of ball.
[tex]{\text{m}} = \frac{{\text{h}}}{{\lambda {\text{v}}}}[/tex] ....... (2)
The value of wavelength is [tex]3.45 \times {10^{ - 34}}\;{\text{m}}[/tex].
The value of velocity is 6.55 m/s.
The value of Planck’s constant is [tex]6.626 \times {10^{ - 34}}{\text{ kg}} \cdot {{\text{m}}^2}{\text{/sec}}[/tex].
Substitute these values in equation (2).
[tex]\begin{aligned}{\text{m}}&=\frac{{6.626 \times {{10}^{-34}}{\text{ kg}}\cdot {{\text{m}}^2}{\text{/sec}}}}{{\left( {3.45 \times {{10}^{-34}}{\text{ m}}} \right)\left( {6.55\;{\text{m/s}}} \right)}}\\&=0.2932{\text{1 kg}}\\&\approx 0.29{\text{3 kg}} \\ \end{aligned}[/tex]
The mass of ball is to be converted into grams. The conversion factor for this is,
[tex]{\text{1 kg}} = {10^3}\;{\text{g}}[/tex]
So the mass of the ball can be calculated as follows:
[tex]\begin{aligned}{\text{Mass of ball}}&=\left({{\text{0}}{\text{.293 kg}}} \right)\left( {\frac{{{{10}^3}\;{\text{g}}}}{{{\text{1 kg}}}}}\right)\\&=29{\text{3 g}} \\ \end{aligned}[/tex]
Therefore the mass of ball is 293 g.
Learn more:
1. Calculation of de Broglie wavelength: https://brainly.com/question/7047430
2. Basis of investigation for the scientists: https://brainly.com/question/158048
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Atomic structure
Keywords: de Broglie equation, m, h, v, wavelength, velocity, mass, planck’s constant, 3.45*10^-34 m, 6.55 m/s, 293 g.
