Question

calculate the mass of a proton having a wavelength 5984Angstron and velocity 3×10^8° meter second​

Answer 1

Answer:

" wavelength=h/mv

so m= h/(wavelength*velocity)

6.6*10^34/{[5894*10(-10)]*3*10*8}

on solving we get:

m=0.000373*10^(-32)

I=h/mc .I stands for wavelength.

so m= h/c l

Hence m=6.626*10^-34/3*10*8*589*10^-9

So m=3.75*10^-36kg

Compare this with atomic mass unit which is of the order of 10^-27.

Hence,mass of proton is not considerable.

Answer 2

Given :

• Wavelength of a proton = 5984 A⁰
• Velocity of proton = 3 × 10⁸ m/s

To find :

• Mass of the proton

Solution :

The relation between (angstroms) A⁰ and m (metres) is given by ,

$\boxed {\rm{1 \: A {}^{0} = {10}^{ - 10} \: m }}$

$: \implies \rm 5984 \: A {}^{0} = 5984 \times {10}^{ - 10} \: m$

Now The relation between Wavelength , mass and velocity is given by ,

$\dag \: \boxed {\rm{ \lambda = \frac{h}{mv} }}$

Where ,

• λ is wavelength
• m is mass
• v is velocity
• h is planck's constant (=6.625 × 10⁻³⁴ Js)

We have ,

• λ = 5984 A⁰ = 5984 × 10⁻¹⁰ m
• v = 3 × 10⁸ m/s
• m = ?
• h = 6.625 × 10⁻³⁴ J.s

By substituting the values ,

$: \implies \rm \: 5984 \times {10}^{ - 10} \: m= \frac{6.625 \times {10}^{ - 34} \: J.s }{m \times 3 \times {10}^{8} \: m {s}^{ - 1} } \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} \: m = \frac{6.625 \times {10}^{ - 34} \: kg.m {}^{2}s {}^{ - 2}.s }{m \times 3 \times {10}^{8} \: m {s}^{ - 1} } \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} \: m = \frac{6.625 \times {10}^{ - 34} \: kg. \cancel{m {}^{2} . {s}^{ - 1}} }{m \times 3 \times {10}^{8} \cancel{m {s}^{ - 1} }} \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} \: m = \frac{6.625 \times {10}^{ - 34} \: kg.m }{m \times 3 \times {10}^{8} } \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} \cancel{m} = \frac{6.625 \times {10}^{ - 34} \: kg. \cancel{m} }{m \times 3 \times {10}^{8} } \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} = \frac{6.625 \times 10 {}^{ - 34} \: kg \times 10 {}^{ - 8} }{3 \times m} \\ \\ : \implies \rm \: 5984 \times 10 {}^{ - 10} = \frac{6.625 \times {10}^{ - 42} \: kg }{3m} \\ \\ : \implies \rm \: 5984 \times {10}^{ - 10} \times 3m = 6.625 \times {10}^{ - 42} \: kg \\ \\ : \implies \rm \: 3m = \frac{6.625 \times {10}^{ - 42} \: kg}{5984 \times 10 {}^{ - 10} } \\ \\ : \implies \rm \: 3m = 1.107 \times {10}^{ - 35} \: kg \\ \\ : \implies \rm \: m = \frac{1.107 \times {10}^{ - 35} \: kg }{3} \\ \\ : \implies \rm \: m = 3.7 \times 10 {}^{ - 36} \: kg$

Hence , The mass of the proton is 3.7 × 10⁻³⁶ kg