A single slit diffraction experiment is performed to determine the slit width using the equation, \( \dfrac{bd}{D} = m\lambda \), where \( b \) is the slit width, \( D \) the shortest distance between the slit and the screen, \( d \) the distance between the \( m^{\text{th}} \) diffraction maximum and the central maximum, and \( \lambda \) is the wavelength. \( D \) and \( d \) are measured with scales of least count of \( 1 \, \text{cm} \) and \( 1 \, \text{mm} \), respectively. The values of \( \lambda \) and \( m \) are known precisely to be \( 600 \, \text{nm} \) and \( 3 \), respectively. The absolute error (in \( \mu \text{m} \)) in the value of \( b \) estimated using the diffraction maximum that occurs for \( m = 3 \) with \( d = 5 \, \text{mm} \) and \( D = 1 \, \text{m} \) is ___.
A dimensionless quantity is constructed in terms of electric charge \( e \), permittivity of free space \( \varepsilon_{0} \), Planck constant \( h \) and speed of light \( c \). If the dimensionless quantity is written as \( e^{\alpha}\varepsilon_{0}^{\beta}h^{\gamma}c^{\delta} \) and \( n \) is a non-zero integer, then \( (\alpha, \beta, \gamma, \delta) \) is given by:
