A nucleus at rest undergoes a decay emitting an α

Question

A nucleus at rest undergoes a decay emitting an α particle of de-Broglie wavelength λ = 5.76 x 10-15 m. If the mass of the daughter nucleus is 223. 610 amu and that of the α particles is 4.002 amu, determine the total kinetic energy in the final state. Hence, obtain the mass of the parent nucleus in amu. ( 1 amu = 931. 470 MeV / c2)

Navjyot Kalra · Accepted Answer

Hello Student,

Please find the answer to your question

Let the reaction be

Here, m_y = 223.61 amu and m_α = 4.002 amu

We know that

λ = h / mv ⇒ m² v² = h² / λ² = p²

⇒ But E.K. = p² / 2m . Therefore K.E. = h² / 2mλ² …(i)

Applying eq. (i) for Y and α, we get

K.E._α = (6.6 x 10^-34)² / 2 x 4.002 x 1.67 x 10^-27 x 5.76 x 10^-15 x 5.76 x 10^-15

= 0.0982243 x 10^-11 = 0.982 x 10¹² J

Similarly (E.K.)_y = 0.0178 x 10^-12 J

Total energy = 10^-12

We know that E = ∆mc²

∴ ∆m = E /c² = 10^-12 / ( 3 x 10⁸)² kg

x 10^-27 kg = 1 amu

∵ 10^-12 / (3 x 10⁸)²kg = 10^-12 amu / 1.67 x 10^-27 x ( 3 x 10⁸)²

= 10^-12 amu / 1. 67 x 9 x 10^-27 x 10¹⁶ = 0.00665 amu

The mass of the parent nucleus X will be

M_x = m_y + m_α + ∆m

= 223. 61 + 4.002 + 0.00665 = 227.62 amu

Thanks
Navjot Kalra
askIITians Faculty

Modern Physics> A nucleus at rest undergoes a decay emitt...

Amit Saxena , 11 Years ago

Navjyot Kalra

LIVE ONLINE CLASSES

A particle is projected in vertical plane such that after 5 seconds its velocity becomes horizontal. The maximum height attained by the projectile from point of projection is n3 m. The value of n is _______. (g = 10 m/s2)

modern physics

Two particles approach each other from very large distance as shown, . if the least separation between the particles is b, what is the speed of M in center of mass frame when particles are closest? (gravity negligible)

modern physics

Can the sum of two equal vectors be equal to either vector

modern physics

A nucleus X¹⁸⁴ at rest emitt alpha particle With kinetic energy 9.0MeV. The product Nucleus is Y. The values of Binding energy per nucleon of alpha particle & Y differ by 1.5MeV. The values of Binding energy per nucleon of X & Y differ by (n÷230) MeV, then n is

modern physics

SUBJECT: PROBLEM BASED ON LINE DETECTION.
Query: How to apply all the filters for line detection on the following piece of image (provided below)? Explain its Observations to comment on its results.

modern physics

Modern Physics> A nucleus at rest undergoes a decay emitt...

Amit Saxena , 11 Years ago

Navjyot Kalra

LIVE ONLINE CLASSES

Other Related Questions on modern physics

A particle is projected in vertical plane such that after 5 seconds its velocity becomes horizontal. The maximum height attained by the projectile from point of projection is n3 m. The value of n is _______. (g = 10 m/s2)

modern physics

Two particles approach each other from very large distance as shown, . if the least separation between the particles is b, what is the speed of M in center of mass frame when particles are closest? (gravity negligible)

modern physics

Can the sum of two equal vectors be equal to either vector

modern physics

A nucleus X184 at rest emitt alpha particle With kinetic energy 9.0MeV. The product Nucleus is Y. The values of Binding energy per nucleon of alpha particle & Y differ by 1.5MeV. The values of Binding energy per nucleon of X & Y differ by (n÷230) MeV, then n is

modern physics

SUBJECT: PROBLEM BASED ON LINE DETECTION.Query: How to apply all the filters for line detection on the following piece of image (provided below)? Explain its Observations to comment on its results.

modern physics

A nucleus X¹⁸⁴ at rest emitt alpha particle With kinetic energy 9.0MeV. The product Nucleus is Y. The values of Binding energy per nucleon of alpha particle & Y differ by 1.5MeV. The values of Binding energy per nucleon of X & Y differ by (n÷230) MeV, then n is

SUBJECT: PROBLEM BASED ON LINE DETECTION.
Query: How to apply all the filters for line detection on the following piece of image (provided below)? Explain its Observations to comment on its results.