Question

Protons can be accelerated in particle accelerators. Calculate the wavelength (in Å)
of such accelerated proton moving at 2.85 x108 ms 1 ( the mass of proton is 1.673 X
10-27 Kg).
​

Answer 1

Answer:

The required answer is 0.00001389 angstroms

GIVEN:

• velocity of proton ,$v=2.85×10^8 m/s$

• mass of proton, $m=1.673×10^-27 kg$

TO FIND:

wavelength,$\lambda$

FORMULA:

according to de broglie equation,

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

where,

• h is the planck's constant.

• its value is ,$h=6.625×10^-34 Js$

SOLUTION:

$\lambda = \frac{h}{mv} \\ \\ \frac{6.625 \times {10}^{ - 34} }{(1.673 \times {10}^{ - 27)}(2.85 \times {10}^{8} ) } \\ \\ = \frac{6.625 \times {10}^{ - 34} }{4.76805 \times {10}^{ - 27 + 8} } \\ \\ = \frac{6.625 \times {10}^{ - 34} }{4.76805 \times {10}^{ - 19} } \\ \\ = 1.389 \times {10}^{ - 34 + 19} \\ \\ \lambda= 1.389 \times {10}^{ - 15} m \\ \\ = 1.389 \times {10}^{ - 5} \times {10}^{ - 10} m \\ \\\lambda = 0.00001389 \times {10}^{ - 10}$

ANSWER:

$\text{wavelength<strong> </strong><strong>of</strong><strong> </strong><strong>proton</strong><strong> </strong><strong>is</strong><strong> </strong><strong> </strong><strong>{</strong><strong>0</strong><strong>.</strong><strong>0</strong><strong>0</strong><strong>0</strong><strong>0</strong><strong>1</strong><strong>3</strong><strong>8</strong><strong>9</strong><strong> </strong><strong>A^</strong><strong>°</strong><strong>}</strong><strong> </strong>}$

ADDITONAL INFORMATION:

• wavelength of an object is inversely proportional to its mass.

• so a body with heavy mass will have negligible wavelength

• hence de broglie's equation is applicable to objects of negligible mass. so their wavelength is appreciable