$z_T=\frac{2a^2}{\lambda},$
$z_T=\frac{\lambda}{1 - \sqrt{ 1 - \frac{\lambda^2}{a^2} }},$
Due to the quantum mechanical wave nature of particles, diffraction effects have also been observed with atoms—effects which are similar to those in the case of light. Chapman et al. carried out an experiment in which a collimated beam of sodium atoms was passed through two diffraction gratings (the second used as a mask) to observe the Talbot effect and measure the Talbot length. The beam had a mean velocity of 1000 m/s corresponding to a de Broglie wavelength of $\lambda_{dB}$= 0.017 nm. Their experiment was performed with 200 and 300 nm gratings which yielded Talbot lengths of 4.7 and 10.6 mm respectively. This showed that for an atomic beam of constant velocity, by using $\lambda_{dB}$, the atomic Talbot length can be found in the same manner.