Two particles A and B are in motion. Wavelength of A is 4×10^-5 m and mass of B is 25% of mass of A. Velocity of B is 50% of velocity of A. Calculate wavelength of B.
Answers
Given:
- Wavelength of A =
- Mass of B= 25% of mass of A
- Velocity of B = 50% of velocity of A
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Need to find:
- Wavelength of B=?
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Solution:
We know,
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Now let's find mass of B,
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Velocity of B,
━━━━━━━━━━━
Now,
Given:
Wavelength of A = 4 \times {10}^{ - 5}4×10
−5
Mass of B= 25% of mass of A
Velocity of B = 50% of velocity of A
━━━━━━━━━━━━━━━━
Need to find:
Wavelength of B=?
━━━━━━━━━━━━━━━━
Solution:
We know,
\lambda \: = \dfrac{h}{mv}λ=
mv
h
{\lambda}_{A} = \dfrac{h}{{m}_{A} \times {v}_{A}}λ
A
=
m
A
×v
A
h
\bold{\purple{\boxed{4 \times {10}^{ - 5} = \dfrac{h}{{m}_{A} \times {v}_{A}}}}}
4×10
−5
=
m
A
×v
A
h
━━━━━━━━━━━
Now let's find mass of B,
{m}_{B} = 25 \: {m}_{A}m
B
=25m
A
\purple{\bold{\boxed{{m}_{B} = \dfrac{25}{100} {m}_{A}}}}
m
B
=
100
25
m
A
━━━━━━━━━━━
Velocity of B,
{v}_{B} = 50 \: {v}_{A}v
B
=50v
A
\boxed{\purple{\bold{ {v}_{B} = \dfrac{50}{100} {v}_{A}}}}
v
B
=
100
50
v
A
━━━━━━━━━━━
Now,
{\lambda}_{B} = \dfrac{h}{{m}_{B} \times {v}_{B}}λ
B
=
m
B
×v
B
h
= \dfrac{h}{ \dfrac{25}{100}{m}_{A} \times \dfrac{50}{100}{v}_{A} }=
100
25
m
A
×
100
50
v
A
h
= \dfrac{h}{ \dfrac{{m}_{A}}{4} \times \dfrac{{v}_{A}}{2} }=
4
m
A
×
2
v
A
h
= \dfrac{8h}{{m}_{A} \times {v}_{A}}=
m
A
×v
A
8h
= 8 \times (4 \times {10}^{ - 5} )=8×(4×10
−5
)
\red{\bold{\boxed{\boxed{\large{= 32 \times {10}^{ - 5} m}}}}}
=32×10
−5
m