What is the wavelength, in meters, of an alpha particle with a kinetic energy of 8.0x10^-13 J. The mass of an alpha particle= 4.00150 amu. Given 1 amu= 1.67x10^-27 kg. (K.E.= 1/2mv^2)

Question

masumanwar · Answer

wave particle duality principles can be applied as hnu=mc^2=E

anonymous · Answer

I don't know how to use that formula

michele_laino · Answer

for example the momentum $p$ of the alpha particle, is:
$$\Large p = \sqrt {2 \cdot m \cdot KE} $$
where $KE$ is its kinetic energy, and $m$ is its mass, namely:
$$\Large \begin{gathered}
  KE = 8 \cdot {10^{ - 13}}joules \hfill \ \
  m = 4.0015 \times {1.67\cdot 10^{ - 2t}} = ...?Kgr \hfill \ 
\end{gathered} $$
therefore, the requested wavelength $\lambda$, is given by means of the formula of De Broglie:
$$\Large \lambda  = \frac{h}{p}$$
where, $h$ is the Planck's constant:
$$\Large  h = 6.62 \cdot {10^{ - 34}}joules \times \sec $$

michele_laino · Answer

oops.. it is:
$$\Large m = 4.0015 \times 1.67 \cdot {10^{ - 27}} = ...?Kg$$