How can you make the image transparent.(no black)
I guess you have the wanted alpha channel as a separate image and the colored version should get it. In the next image both versions are separate layers in the same image:
If you insert a layer mask to the colored version you get normally a white mask like it has happened above.
Select the content of the wanted mask layer and copy it to the clipboard
Click the layer mask icon of the colored version by holding Alt key at the same time. That brings the mask under onscreen editing.
Paste the new mask in place
Disable the wanted mask -layer. and see the result:
You can export as PNG if you want a single layer image which has the mask applied permanently (=as a new alpha channel). I wouldn't apply the mask in Photoshop (= Layer > Layer Mask > Apply) because I see it's a benefit to have the transparency in an editable mask.