To determine which of the given statements is incorrect, let's analyze each statement one by one:
A. The dimension of Planck's constant:
The dimensional formula of Planck's constant [tex]\(h\)[/tex] is given by the product of energy (E) and time (T). Since energy [tex]\(E\)[/tex] has the dimensional formula [tex]\(ML^2T^{-2}\)[/tex], and time [tex]\(T\)[/tex] has the dimensional formula [tex]\(T\)[/tex], the dimensional formula for [tex]\(h\)[/tex] can be derived by multiplying these:
[tex]\[ [h] = [E] \times [T] = ML^2T^{-2} \times T = ML^2T^{-1} \][/tex]
Therefore, the given dimension [tex]\(ML^2T^{-1}\)[/tex] is correct.
B. The formula for calculating the momentum of a photon:
The formula [tex]\(E^2= m^2C^4+ P^2C^2\)[/tex] is the relativistic energy-momentum relation. For a photon, the rest mass [tex]\(m\)[/tex] is zero, so the equation simplifies to:
[tex]\[ E^2 = P^2C^2 \][/tex]
This is also correct, as it accurately represents the relationship between the energy and momentum of a photon.
C. The conversion for 1 acre to square meters:
The given conversion is [tex]\(1 \, \text{acre} = 4047 \, \text{m}^2\)[/tex]. Checking standard conversions:
[tex]\[ 1 \, \text{acre} = 4046.856 \, \text{m}^2 \][/tex]
Rounding this value to the nearest whole number gives approximately [tex]\(4047 \, \text{m}^2\)[/tex], indicating that this statement is essentially correct.
D. None:
Given that the first three statements (A, B, and C) have been verified as correct, the answer that none of the statements is wrong is the correct choice.
Thus, the correct answer to the question is:
D. None
