With the same matched line, three calibration scales move the displayed detector channel. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Scale changes the detector channel
The photon energy stays 5 joules and the offset stays 1 channel. Scale 1 maps the line to channel 6.
channel=1⋅5+1=5+1=6
Scale changes the detector channel
The photon energy stays 5 joules and the offset stays 1 channel. Scale 2 maps the line to channel 11.
channel=2⋅5+1=10+1=11
Scale changes the detector channel
The photon energy stays 5 joules and the offset stays 1 channel. Scale 3 maps the line to channel 16.